bro man 2015
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PaperTRANSCRIPT
Electronic copy available at: http://ssrn.com/abstract=2307229
Liquidity, Style Investing and Excess Comovement of Exchange-Traded Fund
Returns
Markus S. Broman*
First draft: May 20, 2013
This draft: May 12, 2015
ABSTRACT
This study shows that return differences between Exchange-Traded Funds and their underlying
portfolio Net Asset Values β which are claims on the same underlying cash-flows β comove
excessively across ETFs. Excess comovements are highly significant across ETFs in matching
investment styles, negative and generally significant across distant styles. Further tests based on
return reversals suggest that ETF premiums relative to NAV reflect misvaluation primarily in the
ETF, rather than the NAV price, particularly for ETFs in more liquid styles (e.g. small-cap).
Finally, the degree of return comovements is stronger for funds with high commonality in
demand shocks and high liquidity relative to their underlying basket. These findings are
consistent with the idea that liquidity can sometimes be detrimental to pricing efficiency, because
liquidity attracts short-horizon investors that engage in correlated style switching strategies.
JEL Classification: G10, G12, G14, G23
Keywords: ETF, Excess Comovement, Correlated Demand, Liquidity clientele, Style
investing, Market Efficiency.
* Finance Department, Schulich School of Business, York University, 4700 Keele St., Toronto, Ontario
M3J 1P3, Tel: (416) 736-2100 ext. 44655, e-mail: [email protected]. I am grateful to Larry
Harris, Pauline Shum, Yisong Tian, Kee-Hong Bae, Mark Kamstra, Sandy Suardi, Anna Agapova, Jared
DeLisle, Dennis Bams, Kristian Miltersen, Francesco Franzoni, Thierry Foucault, Daniel Andrei and
Akiko Watanabe for discussions and suggestions, as well as seminar participants at York University
(Canada), Ryerson University, Norwegian School of Economics, Aalto University School of Business,
ESSEC Business school, Syracuse University, the 2013 European Financial Management Association
meetings in Reading (U.K.), the 2014 Eastern Finance Association meetings in Pittsburgh (United States),
the 2014 Financial Management Association conference in Maastricht (the Netherlands), the 2014
European Finance Association conference in Lugano (Switzerland), the 2014 Northern Finance
Association conference in Ottawa (Canada) and the 2015 American Finance Association in Boston,
(United States). Responsibility for any errors or omissions, is of course, entirely mine. Β© by the author.
Electronic copy available at: http://ssrn.com/abstract=2307229
1
1 Introduction
Liquidity is generally considered to be beneficial for pricing efficiency because it facilitates
arbitrage. In this study I argue that liquidity can sometimes also be detrimental for pricing
efficiency because liquidity facilitates short-term trading that has the potential to generate excess
comovements among asset returns. In Barberis and Shleifer (2003) investors allocate money at
the style level and engage in short-term style switching for reasons unrelated to fundamentals β
allocating more capital to styles that recently performed well and taking money out of styles that
have done poorly. This type of correlated trading can induce a common factor in the returns of
assets in the same style2.
Investor demand should go first to the securities where the purest play exists and where
liquidity is highest. Exchange-Traded Funds provide investors with easy access to popular
investment styles (e.g. Large, Small, Value, Growth and Sector) at a cost that is on average lower
relative to their underlying basket of securities (Broman and Shum, 2015). Moreover, it is easy to
move money in and out of two different styles with ETFs and to enter into long-short strategies
(e.g. Value-Growth) due to the relatively low short-selling costs of ETFs.
My conjecture is that, due to the ease of investing in investment styles with ETFs and
because of their high liquidity, ETFs attract a clientele of short-term investors with correlated
non-fundamental demand at the style level. Consequently, the returns of ETFs will be more
exposed to a common source of style-based non-fundamental risk relative to their underlying
securities. This relative, or twin-based, comparison allows me to identify excess comovements
by studying common factors in the change in misvaluation, proxied by the return difference
between an ETF and its underlying portfolio Net Asset Value (NAV). This approach is in sharp
contrast to existing studies that investigate anomalous return comovements around βexogenousβ
events, or by relying on a CAPM type model to filter out the fundamental component of returns3.
Moreover, by properly controlling for fundamental drivers of return comovements, I can
examine what affects the degree of excess comovements in order to provide a better
2 Similar predictions arise in preferred habitat model of excess comovement (Barberis, Shleifer and Wurgler, 2005),
which predicts that some investors restrict their trading to a subset of securities and the correlated non-fundamental
demand of these investors is responsible for generating excess comovements. 3 e.g. Barberis, Shleifer and Wurgler (2005), Prinsky and Wang (2006), Green and Hwang (2009), Kumar, Page and
Spalt (2013)
2
understanding of the ETF characteristics, particularly liquidity, that drive a wedge in the clientele
between ETFs and their underlying securities.
An alternative mechanism that can generate excess comovements is differences in the
speed of information diffusion between ETFs and their underlying portfolios. In this case the
high liquidity of ETFs is more likely to attract investors with fundamental (long-term)
information about abstract risk factors. Differences in information diffusion can also arise
mechanically when there is stale pricing in the underlying securities (e.g. in small-cap stocks).
This hypothesis is also known as the information diffusion view of excess comovements (see
Barberis, Shleifer and Wurgler, 2005).
An important distinction between the non-fundamentals-based and the fundamentals-based
view of excess comovement is that the former assumes that style investor have short horizons.
Although the high liquidity of ETFs is beneficial to both long- and short-term investors, I argue
that liquidity benefits short-term investors the most as in Amihud and Mendelson (1986).
Supporting this conjecture, Broman and Shum (2015) show that ETFs with high liquidity relative
to their underlying securities have higher fund flows in the short-term, higher institutional
ownership by short-term (relative to long-term) investors and shorter institutional holding
periods (relative to their underlying baskets). Retail investors are even more likely to be attracted
to ETFs for liquidity reasons because the transaction costs that they face when investing in the
underlying security basket are likely prohibitive.
To make my tests as clean as possible, I focus on a sample 164 physically replicated ETFs
that are traded in the U.S. and that track only U.S. equity indices. These funds have over $540
billion in total assets as of 12/2012 β roughly 85 percent of the total assets of all U.S. equity
ETFs. In contrast to related studies on βtwin securitiesβ; cross-listed stocks (e.g. Gagnon and
Karolyi, 2010), international closed-end funds (Bodurtha, Kim and Lee, 1995), or even domestic
closed-end funds (Lee, Shleifer and Thaler, 1991), my sample is unlikely to be affected by either
non-synchronicity or stale pricing. The former is not a concern since ETFs and their underlying
securities are traded in the same time-zone. Stale pricing is unlikely to occur because both ETFs
and their underlying securities are generally actively traded, with the possible exception of small-
cap stocks. I conduct several tests based on reversals in misvaluation to rule out this possibility.
3
To preview my results, I find significant commonality in misvaluation at the investment
style level (size, valuation and sector): changes in misvaluation (ETF-NAV returns) comove
positively across ETFs in similar styles, and negatively with ETFs in distant styles. To illustrate
the economic magnitude, a one Std. Dev. increase in the own-style misvaluation factor is on
average associated with an increase in daily ETF-NAV return differentials of 55.73 percent of
the Std. Dev. of ETF-NAV returns. The impact of a one Std. Dev. shock to the own-style factor
is also considerable relative to the variability in raw returns at roughly 4 percent4, but declines
with the return horizon to 2.29 and 1.27 percent in weekly and monthly data respectively.
Despite the decline in the magnitude of excess comovements, the results remain highly
significant even in monthly data, which is more consistent with the non-fundamentals based view
of excess comovement as opposed to information diffusion, because the latter predicts that
information is assimilated relatively fast to both ETFs and their underlying securities since both
are liquid and actively traded instruments. I also find some evidence of negative excess
comovements among ETFs in distant styles consistent with style switching across twin styles as
predicted by Barberis and Shleifer (2003).
To provide more direct evidence that changes in misvaluation are in fact driven by
misvaluation in the ETF, rather than the NAV leg, I investigate the source of misvaluation.
Specifically, if an ETF is hit by a positive non-fundamental demand shock that pushes its price
above the underlying portfolio NAV value (positive ETF premium), then we should observe a
reversal in the future ETF returns without any impact on NAV returns. Conversely, if the initial
positive demand shock was driven by positive fundamental news that is absorbed first into ETF
prices, then future NAV returns should be positive as the NAV catches up with a lag and the
ETF return should remain unaffected. The empirical results confirm that ETF premiums have a
negative and significant impact on future ETF returns over a period of three to four days,
consistent with premiums reflecting non-fundamental demand shock. More importantly,
reversals in ETF returns are strongest among small-cap ETFs (the category with the highest
liquidity relative to their underlying basket), which is consistent with the conjecture that liquidity
attract short-term investors with a greater exposure to non-fundamental demand shocks.
Moreover, current ETF premiums also forecast future NAV returns negatively over a four
day period (positive on first day, negative on the remaining days), which is opposite to what the
4 Calculated as π½πππ β ππ‘π(Own style factor)/ππ‘π(Raw return of ETF π), averaged across all ETFs.
4
information diffusion view would predict. Such a negative relationship can, however, arise when
investors experience non-fundamental demand shocks and trade sequentially. In this case
liquidity goes first to the most liquid securities (ETFs) and when liquidity dries up, demand goes
to the next most liquid ETF and so on, until no more ETFs are sufficiently liquid relative to their
underlying securities, in which case the demand goes to the underlying securities.
To provide further evidence that commonality in misvaluation is driven by commonality in
demand shocks, I begin by investigating commonality in turnover and liquidity, which has
previously been linked to correlated trading (e.g. Chordia, Roll and Subrahmanyam, 2000;
Karolyi, Lee and Van Dijk, 2012). I find similar style-based comovements in relative measures
for turnover and liquidity with most of the effect originating from ETF, rather than the NAV leg.
Next, I establish that commonality in demand shocks can predict one-month ahead commonality
in misvaluation, which is consistent with the idea that excess comovements are driven by
correlated non-fundamental demand shocks.
Finally, I investigate the determinants of the degree of commonality in misvaluation and
find that ETFs with more desirable liquidity characteristics (lower quoted spreads, expense ratios
and total misvaluation) have a greater degree of commonality in misvaluation. This is to be
expected if liquidity is what attract short-term traders to ETFs. Controlling for an ETFs liquidity
characteristics, return comovements should also be greater when market-wide arbitrage costs are
high because they leave more βroomβ for excess comovement (Kumar and Lee, 2006; Kumar
and Spalt, 2013). Consistent with this idea, I find that return comovements are higher when
funding liquidity is low, or when market volatility is high.
Understanding what affects asset prices in the ETF market is important due to the potential
for spillovers across markets. Staer (2014) shows that ETF fund flows have a large impact on
underlying stock returns, almost half of which is reversed within a few days. Ben-David,
Franzoni and Moussawi (2014) find that higher ETF ownership of stocks is associated with more
volatile stock returns and a stronger mean-reverting component in stock returns, while Da and
Shive (2013) link higher ETF ownership to stronger underlying stock return comovements. My
conjecture that ETFs attract high-turnover investors with correlated trading needs is consistent
with these findings.
Among the most widely cited evidence in favor of correlated demand-based theories of
excess comovement are the comovements observed around index additions (with other index
5
stocks) and stock splits (with low-priced stocks)5. The critical assumption, that the event is
exogenous remains controversial and has recently been challenged by Kasch and Sarkar (2012)
and Perez, Shkilko and Tang (2012). A broader debate in the literature concerns whether the
observed comovement patterns among small-cap stocks (Banz, 1981) or value/growth stocks
(Fama and French, 1993, 1995) can be explained by common variation in cash flows or discount
rates6; or by unmodeled irrational behavior (see Barberis and Thaler, 2003), and to what extent
limits-to-arbitrage can explain these findings (Brav, Heaton, Li, 2010). My contribution in this
regard is to provide a more controlled experiment that is better suited for separating the two
sources (fundamental vs. non-fundamental) of return comovements.
This paper is also related to a growing literature on the relationship between correlated
trading and return comovements. Kumar and Lee (2006) find not only that retail trades are
systematically correlated, but also that such trades can help explain some of the anomalous
return comovements among stocks with high arbitrage costs. Correlated retail demand has also
been linked to investorsβ tendency to place similar speculative bets (Dorn, Huberman and
Sengmueller, 2008). Kumar, Page and Spalt (2013b) show that stocks with lottery-like feature
comove too much with one another due to the correlated trading activity of gambling-motivated
investors. Greenwood (2007) constructs a simple trading strategy that bets on the reversion of the
prices of over-weighted Nikkei 225 stocks that comove too much in the short-run and finds this
trading strategy to yield significant risk-adjusted profits.
The article proceeds as follows. Section 2 provides some background information on ETF
arbitrage and institutional details. Section 3 provides the theoretical framework and presents the
main testable implications. Section 4 describes the data, defines the key variables and presents
summary statistics. Section 5 presents the empirical tests for excess comovement based on an
analysis of commonality in ETF misvaluation. Section 6 establishes that ETF premiums mainly
reflect misvaluation in the ETF, rather than NAV leg. Section 7 documents that measures of ETF
demand shocks also exhibit style-based comovement and that the degree of common demand
shocks can predict commonality in misvaluation, along with ETF characteristics associated with
higher liquidity. Section 8 concludes.
5 See e.g. Barberis, Shleifer and Wurgler (2005), Green and Hwang (2009), Kumar, Page and Spalt (2013).
6 See e.g. Fama and French (1993), (1995); Campbell, Polk and Vuolteenaho (2009); Campbell et al. (2013)
6
2 Background on ETF arbitrage and institutional details
ETFs have an open-ended structure via the share creation and redemption process that facilitates
arbitrage. This process is only available to some institutional investors (called Authorized
Participants, or APs), which have signed an agreement with the ETF sponsor. APs can buy or
sell ETF shares in bundles (or creation units) directly from the ETF sponsor in exchange for the
underlying basket of securities at the end of the trading day (at 4 P.M. EST). Although this
process is limited to APs (typically market makers, broker/dealers or large institutions), they can
also create (or redeem) shares directly for their clients who wish to transact in ETFs.
To illustrate the arbitrage process via the share creation mechanism, consider a situation
where the ETF is trading at a premium (ETF price is above the NAV). An AP would then buy
the underlying basket (at the NAV), exchange the basket for new ETF shares with the ETF
sponsor and sell the newly created shares on the secondary market. The process works in reverse
when the ETF is trading at a discount (ETF price is below the NAV).
The direct costs of creating ETF shares are small for U.S. equity funds (the focus of this
paper). The size of a creation unit is typically 50,000 or 100,000 shares with dollar values
ranging from $300,000 to $10 million. The fixed creation costs range from $500 to $3,000. For
SPY, the worldβs largest and most actively traded ETF tracking the S&P 500, the fixed fee of
$3,000 amounts to about 5 bp for one creation unit worth $6 million, or 1 bp for five creation
units worth about $30 million (Petajisto, 2013). For a sample of equity U.S. ETFs7, Broman and
Shum (2015) report that share creations/redemptions occur on 30.9 (22.7) % of trading days on
average (median) and conditional on such days, the magnitudes are $69.6 million ($12.4 million)
or 244.3 percent (27.4 percent) of daily dollar volume. These magnitudes indicate that APβs
frequently create/redeem multiple creation units at a given point in time, possibly to reduce costs.
Arbitrage activity is also undertaken by market participants other than APs, such as hedge
funds and high-frequency traders (Marshall, Nguyen, and Visaltanachoti, 2013). For instance,
when the ETF is trading at a premium, an investor can purchase the underpriced asset (NAV),
short-sell the overpriced asset (ETF) and wait for prices to converge to realize an arbitrage profit.
ETF prices can also be arbitraged against other ETFs (Marshall, Nguyen, and Visaltanachoti,
2013; Petajisto, 2013) or against futures contracts (Richie, Daigler, and Gleason, 2008).
7 Their sample is identical to mine. More details appear in the data section.
7
3 Theoretical framework and testable implications
The theoretical channel for excess comovement in ETF returns relies on correlated demand,
clientele effects and limited arbitrage. In the model by Barberis and Shleifer (2003), investors
allocate funds at the style level (e.g. small or value) as opposed to at the individual asset level,
moving into styles that have performed well in the past, and out of styles that have performed
poorly. The strong demand for investment styles is evident from the large number of ETFs,
mutual funds, and hedge funds that follow distinct styles and which are used by both individual
and institutional investors8. If some of these style investors are also noise traders with correlated
sentiment (e.g. Baker and Wurgler, 2006), then coordinated shifts in investor preferences across
investment styles (e.g. from value to growth) will induce a common factor in the returns of assets
in the same style. In this case, the return of security i belonging to style K is given9:
, , , where i t i t i K tR CF i K (1)
The first component reflects fundamental cash-flow news (βπΆπΉπ,π‘), which is often characterized
via an asset pricing model such as the CAPM or the intertemporal CAPM (Merton, 1973). The
second component reflects common demand shocks for securities in style K, or noise-trader
sentiment as in Barberis and Shleifer (2003). Another intepretation of Eq. (1) is that some
investors focus their trading on ETFs within a specific style giving rise to preferred habitats (see
Barberis, Shelifer and Wurgler, 2005). In this case βππΎ,π‘ captures changes in sentiment, risk-
aversion or liquidity needs of the style investors in habitat K. In line with Greenwood (2007), I
refer to both intepretations as the non-fundamentals based view of excess comovement.
Investor demand should go first to the securities where the purest play exists and where
liquidity is highest. Exchange-Traded Funds provide investors with easy access to popular
investment styles at a cost that is on average lower relative to their underlying basket of
securities (Broman and Shum, 2015). Moreover, it is easy to move money in and out of two
different styles with ETFs and to enter into long-short strategies (e.g. Value-Growth) due to the
relatively low short-selling costs of ETFs10
.
8 see e.g. Brown and Goetzmann (1997); Fung and Hsieh (1997); and Chan, Chen, and Lakonishok (2002)
9 see Eq. (4) in Barberis, Shleifer and Wurgler (2005) Eq. (4), and Eq. (19) in BSW (2002) in the working paper
10 βNo Shortage of Share Lendingβ featured in Journal of Indexes, February 17, 2010.
8
My conjecture is that, due to the ease of investing in investment styles with ETFs and
because of their high liquidity, ETFs attract a clientele of short-term investors with correlated
non-fundamental demand for investment styles. Hence, the returns of ETFs in similar styles will
comove excessively β i.e. after accounting for variation in ETF returns due to common
fundamentals β with one another. To arrive at a testable hypothesis, I first take the return
difference between ETF i and its underlying portfolio Net Asset Value (NAV):
, , , , , ,
ETF NAV ETF NAV ETF NAV
i t i t i t i t i K t i K tR R CF CF (2)
where i, j β K
π π = return for ETF i or underlying portfolio NAV at time t
πΎπ = exposure to common demand shocks of ETF i or its portfolio NAV
The return difference (2) can be intepreted as proxy for the change in misvaluation11
because
ETFs and their underlying portfolio are both claims to the same underlying cash-flows. Hence,
the fundamental cash-flow terms should cancel out (βπΆπΉπ,π‘ β βπΆπΉπ,π‘ = 0). In section 5.3, I also
confirm that the relationship between changes in misvaluation and commonly used systematic
risk factos is economically weak, which is also why I attribute most of the variation in Eq. (2) to
differences in temporary demand shocks. Despite the enhanced pricing efficiency of ETFs via
the share creation mechanism, misvaluation can persist temporarily because arbitrage remains
limited (more in the next section).
The testable implication of style-based excess comovement is that there is commonality in
misvaluation. Specifically,
Hypothesis 1: Changes in misvaluation of any two ETFs in the same style is positively
correlated, ππππ(π ππΈππΉ β π π
ππ΄π, π ππΈππΉ β π π
ππ΄π) > 0, because ETF i and j are both excessively
exposed to common style-specific demand shocks (πΎππΈππΉ β πΎπ
ππ΄π > 0 πππ πΎππΈππΉ β πΎπ
ππ΄π > 0).
Commonality in misvaluation can also arise for other reasons. First, fundamental (long-
term) demand may also go first to securities where the purest play exists and where liquidity is
highest. Hence, commonality in misvaluation can arise if fundamental news about abstract risk-
factors is incorporated first into ETF prices. This is also known as the information diffusion view
of excess comovement (see Barberis, Shleifer and Wurgler, 2005). In contrast, the argument that
11
The change in misvaluation is equivalent to the change in ETF premium, defined more formally in section 4.2.
9
ETFs attract short-term investors with correlated non-fundamental demand relies on liquidity
clienteles, formalized by Amihud and Mendelson (1987). Their model predicts that short-horizon
investors self-select into more liquid assets, such as ETFs. Supporting this conjecture, Broman
and Shum (2015) show that the liquidity of ETFs (relative to their underlying securities) predicts
fund flows strongly over short horizons (weekly and monthly), while over longer horizons
expense ratios matter the most. Amongst institutional investors, the authors also show that funds
with higher relative liquidity experience increased ownership by short-term investors relative to
long-term, more institutional buying and more selling over the following quarter, and shorter
holding periods.
As for retail investors, the argument for liquidity clienteles is even stronger because the
transactions costs that they face when investing in the underlying security basket are likely
prohibitive in comparison to ETFs. Moreover, ETFs generally have lower expense ratios than
even their cheapest retail mutual fund counterparts. Retail investors do pay attention to salient
trading costs such as front-end loads and commissions (Barber, Odean and Zheng, 2005) as well
as expense ratios (Grinblatt et al., 2013) in the case of mutual funds. For ETFs, the most salient
costs are likely to be quoted spreads and expense ratios, both of which are widely disseminated,
while commissions are generally small, and sometimes even close to zero12
.
One way to separate the causes of commonality in misvaluation is to investigate its degree
of persistence. According to the information diffusion view, commonality in misvaluation is
unlikely to persist for long (e.g. over a week or a month) because both ETFs and their underlying
securities are liquid and should therefore incorporate news relatively fast (e.g., iShares S&P500
Growth ETF (TIC: IVW) vs. the underlying S&P 500 growth stocks). In contrast, the non-
fundamental based view suggests that excess comovement may persist over longer horizons (e.g.
monthly or quarterly) because styles go through cycles (Barberis and Shleifer, 2003). Empirical
evidence also suggests that investors allocate funds based on past relative style performance
evaluated over monthly and quarterly periods (Broman and Shum, 2015).
Another way to disentangle the two stories is to directly examine the source of
misvaluation (ETF vs. NAV). The non-fundamentals based view predicts that ETFs are hit by
temporary demand shocks that subsequently revert.
12
Many ETFs have free commissions: for a list see http://etfdb.com/type/commission-free/all/.
10
Hypothesis 2a: Current ETF premiums (ETF-NAV price deviations) predict future ETF returns
negatively, while future NAV returns remain unaffected.
In contrast, the information diffusion view predicts that ETFs impound fundamental
information first, while their underlying securities (NAV) catch up with a lag:
Hypothesis 2b: Current ETF premiums (ETF-NAV price deviations) predict future NAV returns
positively, while future ETF returns are not affected.
Differences in information diffusion can also arise when there is stale pricing in the
underlying securities. In this case information is incorporated first into ETF prices by definition,
which would give the appearance of commonality in misvaluation. Stale pricing could be a
concern for some small-cap stocks, but not for actively traded large-cap stocks. To rule out this
possibility, I examine whether the results for commonality in misvaluation continue to hold
among ETFs that hold underlying securities that are not prone to stale pricing (e.g. large-cap).
Finally, if the degree of commonality in non-fundamental demand shocks varies across
ETFs or over time, then this variation should be positively related to the amount of commonality
in misvaluation (Greenwood, 2007; Greenwood and Thesmar, 2011). Moreover, with an
appropriate adjustment for total misvaluation, the exposure of ETF i to common non-
fundamental demand shocks (or the degree of commonality in misvaluation) should also be
stronger for more liquid ETFs because they are more likely to attract short-term investors.
Hypothesis 3: The degree of commonality in misvaluation is positively related to the degree of
commonality in non-fundamental demand and the liquidity characteristics of ETF i.
3.1 Additional assumption: Limits-to-Arbitrage
Without limits-to-arbitrage shocks to asset prices should revert instantaneously. In reality
arbitrage remains limited by transactions costs, holding costs and other implicit restrictions (e.g.
short-selling constraints). As for transactions costs, both ETF and underlying portfolio spreads
matter because arbitrage trades require access to both markets. Price impact is also of particular
concern. Staer (2014) reports that a 1 Std. Dev. increase in aggregate share creations ($2.47
billion) is on average associated with a 52 bp concurrent increase in market returns; almost 40 %
of the initial price impact reverts within five days.
11
The potentially high price impact costs of ETF share creations combined with the large
size of typical creation events (Broman and Shum, 2015) indicate that APs might need several
days to accumulate a position that is large enough to offset the creation without undue price
impact. This makes it harder to trade on small price deviations by using the share creation
process. Traditional long-short arbitrage trades with smaller trade sizes can be used to avoid
some of the price impact costs. However, such arbitrage trades are exposed to holding costs
(costs that accrue every period a position), especially idiosyncratic risk, for as long as the
arbitrage trade is kept open (see Pontiff, 2006).
Greenwoodβs (2005) model can be used to justify limits-to-arbitrage further. In their model
market-makers (or APs in the ETF market) are risk-averse and require compensation for
providing liquidity. Thus, when a positive shock hits the ETF market, APs absorb the liquidity
demand by shorting the ETF and simultaneously hedging their short ETF position by purchasing
the underlying basket. Because APs are risk averse, they require compensation for the additional
inventory that they are taking on. Similar predictions arise in Cespa and Foucaultβs (2014) model
with multiple investor classes and some degree of market fragmentation. Ben-David, Franzoni
and Moussawi (2014) discuss a dynamic extension of Cespa and Foucaultβs (2012) model to
further justify temporary price discrepancies between identical assets.
4 Data
My data selection starts with all U.S. traded Exchange-Traded Funds that exist both in
Bloomberg and in Morningstar Direct. I keep funds that i) invest in U.S. equity, ii) are physically
replicated and βpassivelyβ managed and iii) have at least 3 years of data available13
. The second
criterion, which excludes actively managed and synthetically replicated ETFs, is particularly
important for this study. Active ETFs include βsmart betaβ funds that give investorβs access
fundamentally-weighted indices and funds based on proprietary underlying indices. These are
excluded because they are less likely to represent pure plays on investment styles, they may be
chosen by investors because of their investment strategy or manager performance and also
because their holdings change frequently making it more difficult to measure their NAVs and
mispricing. Synthetically replicated ETFs (i.e. leveraged, inverse and futures-based ETFs) are
13
I exclude the first 6 months of a funds history since the data can be unreliable (Broman and Shum, 2015), leaving
me with an estimation sample of at least 2.5 years.
12
excluded because their holdings change frequently, and because arbitrage is more risky as share
creations are settled in cash14
rather than in-kind. These three exclusion criteria decrease the
sample of ETFs from 363 to 224 to 164. In terms of assets under management (AUM), the total
AUM of U.S. ETFs was $632 billion in September 2012 according Blackrock (2012), while the
AUM of my 164 funds was $540 billion. Given the dramatic expansion in scope and size of the
ETF market in the last five to ten years, earlier data may not be as representative of current
market conditions, which is why I decided to focus on a recent sample period, from January 2006
to December 2012. I also conduct robustness tests on a sample starting in June 2002.
The sample of ETFs, along with NAVs15
, shares outstanding and prices for the underlying
indices, is obtained from Bloomberg. To ensure the reliability of NAV prices from Bloomberg, I
cross-check the NAV data with CRSP Mutual Fund Database. My second source is CRSP, which
I use to obtain price, return and volume data for all funds.
Third, I use the ubiquitous 3-by-3 Morningstar style classification (Small-, Mid- and
Large; Value-Blend-Growth) to identify the investment style of a fund. I use the size and
valuation styles based on the evidence in Froot and Teo (2009) and Kumar (2009) that both retail
and institutional investors allocate capital at the size and value-growth level. The Morningstar
classification has three key advantages. First, it coincides with the dichotomy often used by
practitioners and many ETFs are named after their Morningstar style analogs (e.g. SPDR S&P
600 Small-Cap Value or iShares Russell 3000 Growth fund). Investors do pay attention to fund
names as illustrated by Cooper, Gulen and Rau (2005). They show that mutual funds that take
rename their fund to match the current βhot style βsubsequently experience abnormal inflows,
even when the name change is unrelated to performance or any real change in holdings to match
the new style. Second, Morningstar is a leading fund information provider and its classification
system is publicly available. Third, the Morningstar style classification is updated monthly and it
is based entirely on firm characteristics, which yields more stable style classifications over time
as opposed to a latent variable approach based on the Fama and French (1993) factor loadings.
Table 1 gives snapshots of the sample used in this study. At the beginning (01/2006), my
sample contains 95 ETFs with $199.82 billion in AUM. Subsequently there are 156 ETFs with
14
With cash settlement arbitrageurs are exposed to idiosyncratic risk because many ETFs have a cut-off time in the
afternoon to submit creation orders implying that arbitrageurs do not get to see the end-of-day NAVs before making
the decision to trade. 15
For ETFβs by the iShares provider I use the NAV data that is directly available from their website as they contain
fewer data errors, as suggested by Petajisto (2013).
13
$257.55 billion in AUM (06/2009), and 164 ETFs with $540.01 billion at the end of the sample
(12/2012). Roughly half of the funds are in diversified non-sector styles, while the rest are sector
ETFs. Among the non-sector ETFs and within each size-category, the number of blend funds
(neither value, nor growth) is roughly equal to the number of value and growth funds combined.
Sector ETFs are generally much smaller and account overall for only one third of the total AUM.
According to Bloomberg, 142 ETFs are fully replicated (i.e. hold more than 90 percent of the
securities in the underlying index), while the remaining 22 use physical sample replication.
[Table 1]
4.1 Key variables
ETF misvaluation is typically measured by the premium, or the log-difference between the
market price of an ETF and the market value of the ETFβs portfolio on a per-share basis
(NAV16
):
, , ,ln β lnE N Ei t
TF NAVi t i tP P P (3)
where: ππ,π‘πΈππΉ = bid-ask midpoint price for ETF i at the end of day t,
ππ,π‘ππ΄π = Net Asset Value per share for ETF i on day t
Hypothesis 1 predicts that changes in misvaluation, as measured by the ETF-NAV return
difference π π,π‘πΈβπ, contain a common factor at the style level. When log-returns are used, π π,π‘
πΈβπ
corresponds to the change in premium. I will use log-returns throughout this study to keep the
link clear between return differences and changes in premium.
The data contains a handful of extreme observations and other outliers that need to be dealt
with. Premiums greater than 20 % are mainly due to data errors (Petajisto, 2013), and are
therefore discarded. In some cases the NAV prices from Bloomberg represent stale values from
the previous trading day, in which case I use the NAV price obtained from the CRSP Mutual
Fund Database. Moreover, when the premium based on midpoint prices is more than ten
percentage points greater in absolute terms than the premium based on closing prices, I use the
latter instead. Finally, levels and changes in premiums are winsorized fund-by-fund at 5 Std.
Dev. from the mean to reduce the impact of any remaining outliers.
16
NAV also includes accrued income from securities lending, underlying stock dividends and cash.
14
4.2 Descriptive statistics
Table 2 provides descriptive statistics for ETF premiums and ETF-NAV returns (changes in
premiums). Both are zero on average, and at the median, which suggests that ETFs are overall
efficiently priced. There is, however, considerable variation around the mean as indicated by the
standard deviation of 0.09 % and 0.12 % for the level and change in premiums. The extreme
right and left tails (1 and 99 percentiles) are roughly +/- 27 bps for levels of premiums, and +/-
37 % for changes in premiums. Another way to illustrate the magnitude of misvaluation is to
calculate the variability in changes in misvaluation relative to the variability in raw ETF returns,
or ππ·(π π,π‘πΈβπ)/ππ·(π π,π‘
πΈππΉ). This equals a considerable 7.4 percent on an equally-weighted basis.
These numbers are based on mid-point ETF prices at the end of the day. In contrast, the
βactualβ premiums based on closing prices are almost twice as volatile indicating that the true
cost of trading against ETF misvaluation can be much higher. I use mid-point prices in order to
mitigate concerns about the illiquidity of the shares of smaller ETFs (Engle and Sarkar, 2006).
[Table 2]
5 Empirical tests of excess comovement
Commonality in misvaluation at style style level (Hypothesis 1) predicts a positive correlation
between changes in misvaluation of ETF i (π ππΈππΉ β π i
ππ΄π) and ETF j (π ππΈππΉ β π π
ππ΄π), because both
ETF i and j are exposed to common non-fundamental demand shocks at the style level (i, j β K).
This hypothesis can be conveniently tested in the context of the following regression:
, 1 , , , , , ,E N E N E N E Ni t t i t i O OWN t i DI DIST t i tR E R R R e
(4)
where: π π,π‘πΈβπ = π π,π‘
πΈππΉ β π π,π‘ππ΄π , π β πΎ
π πππ,π‘πΈβπ = own-style misvaluation factor, β π€π,π‘(π π,π‘
πΈππΉ β π π,π‘ππ΄π)
π½π=1 , π β πΎ, π β π
π π·πΌππ,π‘πΈβπ = distant-style misvaluation factor, β π€π,π‘(π π,π‘
πΈππΉ β π π,π‘ππ΄π)πΏ
π=1 , π β πΎ
π€π,π‘ = weight for ETF j at time t
Hypothesis 1 predicts a positive correlation between the change in misvaluation of ETF i (π π,π‘πΈβπ)
and the own-style misvaluation factor (π πππ,π‘πΈβπ , π½π,π > 0). Note that the factor excludes ETF i to
avoid inducing a spurious correlation. As discussed in the previous section, some style
dimensions only have a few funds (e.g. 3 ETFs with a Small-Value classification). In order to
15
obtain a parsimonious metric for the own-style factor, and to avoid producing noisy factors based
on a few funds, I use the following weights (π€π,π‘) in constructing the own-style factor: equal
weight is given to funds that match both style dimensions (size and valuation), and half the equal
weight to funds that are in adjacent styles. For instance, if ETF i is Large-Value, then adjacent
styles include Mid-Value and Large-Blend. Blend funds (neither value, nor growth) are matched
only by their size category. This approach is used for all diversified non-sector ETFs.
The Morningstar 3-by-3 style classification only considers size and valuation, while sector
(or industry) styles may also be important. Froot and Teo (2008) show that institutional investors
reallocate capital across three style dimensions (size, valuation and industry), while Choi and
Sias (2009) provide evidence of industry herding among institutional investors that is distinct
from, and at least equally important to, herding by size and valuation styles. For sector ETFs it
may therefore be important to account for all three style dimensions. In constructing the own-
style factor for sector ETFs, I therefore give equal weight to other funds in the same industry,
half the equal weight to any fund in the same size and valuation style and one fourth of the equal
weight to any fund in adjacent Morningstar 3-by-3 styles. For the matching by Morningstar 3-by-
3 style, I do not differentiate between sector and non-sector ETFs.
In the style investing model of Barberis and Shleifer (2003), investors increase their
allocation to a particular style (say Value) after it has outperformed its distant style (Growth).
This switch in allocations is financed either by selling securities in every other style (everything
except Value), or by selling securities only in the distant style. In the latter case, the authors
show that returns of security i comove excessively and positively with the returns of other
securities in the same style (here π½π,π > 0), and negatively with other securities in the distant style
(here π½π,π·πΌππ < 0). To allow for this possibility, I also include a distant-style misvaluation factor
in regression (4). As with the own-style factor, the distant-style factor is specific to ETF i and it
is based on the weighted average ETF-NAV return of other ETFs in distant styles (relative to i).
The following weights (π€π,π‘) are used: equal weight is given to funds that are in distant styles
(along both the size and valuation dimensions) and half the equal weight is given to funds that
are in styles adjacent to the distant style. For instance, if ETF i is Large-Value, then Small-
Growth is the distant style (equal-weight) and Mid-Growth and Small-Blend (half the equal
16
weight) are in styles adjacent to Small-Growth. For mid-cap funds I consider large and small to
be equally distant. Hence, the distant style of Mid-Value is Small-Growth and Large-Growth17
.
I model the conditional expectation for the ETF-NAV return in regression (4) as follows:
, 1 , 1E N E Ni t i i i tE R P (5)
I include the lagged premium (ππ,π‘β1πΈβπ) to account for mean-reversion in the dependent variable
18.
This is important because changes in premiums are by definition mean-reverting as the level is
stationary. In other words, when ETF i is overpriced relative to its underlying portfolio NAV
(ππ,π‘β1πΈβπ > 0), arbitrageurs will buy the underpriced basket of securities and sell the overpriced
ETF, which will induce a correction in misvaluation (π π,π‘β1πΈβπ < 0). A similar approach is used in
Hardouvelis, Porta and Wizman (1994) in their study of the Closed-End Fund discounts and
premiums. The results are not sensitive to including the lagged level of premiums. If anything,
the results are weaker with the premium included.
I run time-series regressions of (4) separately for each ETF using all available observations
and report the mean of the estimated coefficients across all ETFs. In calculating the standard
error for the mean coefficient, I take into account the cross-equation correlations in the estimated
coefficients following Hameed, Kang and Viswanathan (2010):
,
1 1 1 1,
1 1. . . .
N N N N
i i i j i j
i i i j j i
Std Dev Std Dev Var Var VarN N
(6)
where βπππ(π½π) = the White standard error of the coefficient
ππ,π = the estimated correlation between the residuals for ETF i and j.
5.1 Results: style-based commonality in misvaluation
The main results for commonality in misvaluation at the style level (regression (4)) are given in
Table 3. The results are reported separately for the daily, weekly and monthly horizons. For
weekly and monthly data, I require at least 75 percent valid daily observations in each period.
[Table 3]
17
The results also hold if I construct own- and distant-style factors by matching on both the size and valuation styles
while disregarding adjacent styles, or if I disregard the industry styles and match all ETFs (whether sector or non-
sector) based on their size and valuation characteristics. 18
The dependent variable is the ETF-NAV return or the change in premiums π π,π‘πΈβπ = ππ,π‘
πΈβπ β ππ,π‘β1πΈβπ, see section 4.2.
17
The results in Table 3 for the daily horizon show not only that the own-style betas are on average
positive and significant, but also that more than 95 percent of the betas are positive and
(individually) significant. The economic magnitudes are also considerable. To illustrate, a one
Std. Dev. increase in the own-style misvaluation factor is associated with a 6.99 bps increase in
ETF-NAV returns. The proportional impact, π½πππ β ππ‘π(π πππ,π‘πΈβπ )/ππ‘π(π π,π‘
πΈβπ) is also considerable
at 55.73 percent on average indicating that (loosely speaking) almost half of the variation in
changes in misvaluation is driven by the own-style misvaluation factor. The economic
magnitudes, in terms of the proportion of common variation in misvaluation, remains very
similar at weekly and monthly horizons. This finding is more consistent with the non-
fundamentals based view of excess comovement as opposed to information diffusion (or stale
pricing), because the latter predicts that information is assimilated relatively fast to both ETFs
and their underlying securities since both are liquid instruments.
Since the price pressure associated with non-fundamental demand shocks is temporary, the
strength of excess comovements should, on the one hand, decline with the length of the return
horizon. On the other hand, if there is some persistence in demand shocks combined with limits-
to-arbitrage, excess comovements may persist over longer horizons. To better assess whether
excess comovements remain economically important over longer horizons, I recompute the
proportional impacts as π½πππ β ππ‘π(π πππ,π‘πΈβπ )/ππ‘π(π π,π‘
πΈππΉ). This metric tells us how important
common misvaluation is relative to the variability in raw returns. In daily data, common
misvaluation accounts for roughly 4 percent of the variability in raw returns. This effect declines
to 2.29 percent in weekly data, and to 1.27 percent in monthly. Thus, while there is some
persistence in the degree of commonality in misvaluation even over monthly horizons, the
importance of common misvaluation declines over longer horizons consistent with arbitrage
forces playing a role.
In the style investing model the distant-style beta should be negative if investors engage in
style switching between two uniquely identified twin-styles. Consistent with this idea, the
distant-style betas are negative and significant, although their economic magnitude is only one
tenth of those for the own-style beta. This may indicate that investors do not exclusively sell
securities in distant-styles in order to finance a purchase of own-style securities when they have
performed well. Nevertheless, the findings indicate that the own-style misvaluation factor based
18
on size and valuation for non-sector ETFs, and sector, size and valuation for sector ETFs is a
sufficient metric to capture all of the relevant style-based comovements in misvaluation.
The level of premiums predicts changes in premiums negatively consistent with mean-
reversion taking place (ππ < 0 in (5)). When premiums are stationary, the coefficient on ππ,π‘β1πΈβπ
should theoretically equal -1 if shocks to premiums fully revert over one period, instead there is a
considerable degree of heterogeneity in the coefficient estimates with the 5th
, 50th
and 95th
percentiles at -0.85, 0.49, -0.26 respectively at the daily horizon. This suggests that, in the cross-
section of funds, the degree of mean-reversion is generally in the range from 26 to 85 percent.
Finally, it is also important to remember that the economic magnitudes documented here
are conservative because we are making a relative comparison between ETFs and NAVs.
Specifically, regression (4) identifies the relative magnitude of excess comovement (πΎππΈππΉ β πΎπ
ππ΄π
in Eq. (4)). The total amounts (πΎππΈππΉ and πΎπ
ππ΄π) can be bigger if both ETFs and NAVs are hit by
non-fundamental demands, which is likely to occur because ETFs may not have sufficient
liquidity to absorb all of the liquidity-demand by short-term investors. I will revisit this issue and
provide some supporting evidence to this conjecture in section 6.
5.2 Results: sub-samples
Table 4 provides additional sub-sample results for commonality in misvaluation. If stale pricing
is affecting the results, then we should expect the results to be mainly driven by small-cap ETFs
whose underlying stocks may not always be actively traded. In contrast, I find that the degree of
commonality in misvaluation is relatively similar across small-, mid- and large-cap ETFs. The
raw coefficient estimates for the own-style beta are 0.843, 0.828 and 0.957 for large-, mid and
small-caps respetively. Similar patterns are also observed for the proportional impact of common
misvaluation relative to raw returns ( π½πππ β ππ‘π(π πππ,π‘πΈβπ )/ππ‘π(π π,π‘
πΈππΉ) ): 4.52, 3.84 and 5.50
percent for large-, mid- and small-cap ETFs. Given the strength of the results for large- and mid-
caps, stale pricing is unlikely to be a concern here. The somewhat stronger results for small-cap
ETFs is also consistent with my conjecture that liquidity faciliates excess comovements because
small-cap ETFs are on average the most liquid (relative to their underlying securities) and are
therefore more likely to attract short-term investors (Broman and Shum, 2015).
[Table 4]
19
Among the various styles, the results are strongest for value ETFs both in regards to the
own-style comovements (π½π,πππ = 1.037), as well as the distant styles comovements (π½π,π·πΌππ = -
0.173). The results for growth ETFs are weaker than for value ETFs, but similar to blend funds.
The weaker results for blend funds, despite their higher overall liquidity, is consistent with the
idea that growth and value ETFs are more attractive to style investors because they represent
pure plays on investment styles. The results for sector ETFs also hold strongly, although the
comovements are slightly weaker than for non-sector funds (π½π,πππ= 0.774) most likely due to
the difficulty of constructing precise own-style misvaluation factor based on three distinct styles.
Finally, sub-sample results by time-period show that the own-style betas have generally
increased over time from 0.590 in the period prior to the main sample (06/2002-12/2006), to
0.724 during the pre-financial crisis period (12/2006- 07/2008), to 0.884 during the crisis period
(08/2008-03/2009) and to 0.799 in the post-crisis period (03/2009-12/2012). This pattern is
consistent with a greater use of ETFs by short-term investors with non-fundamental demand as
the overall liquidity of ETFs has increased over time (see Figure 1, in Broman and Shum, 2015).
5.3 Robustness: Exposure to systematic risk
Differences in systematic risk between ETFs and their underlying portfolios might be able to
explain the style-based commonality in misvaluation documented earlier. To investigate this
possibility, I regress ETF-NAV returns on the Fama and French 3-factors (MKT, SMB and
HML19
) and the lagged premium to control for mean-reversion in ETF-NAV returns.
[Table 5]
Table 5 shows that daily ETF-NAV returns are negatively and significantly exposed to the
market factor (holds for the average ETF in every style); large-cap ETFs have a positive and
significant exposure to SMB, small-caps have a negative and marginally significant exposure to
SMB, while ETFs in every style are negatively and significantly exposed to HML (except for
Growth ETFs). At the daily level the R2 increases by roughly 8 percent compared with the
baseline model that only includes that lagged premium. A decomposition of R2 reveals that most
of this increase is due to the negative exposure of ETF-NAV returns on the market factor. These
19
It is possible that ETF-NAV returns are correlated with SMB and HML if these return premiums are related to
correlated non-fundamental demand. However, identification of this relationship is likely to be weak given that
SMB and HML are not filtered from fundamental sources of risk.
20
results, particularly the uniformly negative exposure on the market factor, are not easy to
reconcile with the style-based commonality in misvaluation documented earlier, nor do the
results line up with the explanation that ETF returns are fundamentally more risky relative to
NAV returns. Moreover, these findings disappear at lower return horizons.
Another possibility is that ETFs are differentially exposed to systematic liquidity risk,
especially because there are large differences in liquidity between the ETF and its underlying
portfolio. This story is, however, unlikely because recent evidence on the pricing of liquidity risk
in U.S. stocks suggests that the characteristic liquidity premium has declined considerably over
time and is priced only among the smallest stocks, while systematic liquidity is priced primarily
among NASDAQ stocks (Ben-Rephael, Kadan and Wohl, 2013). In contrast, my results are not
driven by small-cap ETFs. To formally investigate this issue I augment the Fama-French 3-factor
model with the market-wide funding liquidity factor based on Hu, Pan and Wang (2013), which
is available at the daily level from the authorβs website. In specification (b) I show that HPWβs
funding liquidity variable enters with a positive and significant coefficient for large-cap ETFs,
but not for small-caps as we might have expected. As before, the results are insignificant at lower
horizons. Thus, differences in systematic risk are unlikely to be able to explain the comovement
patterns documented earlier among ETF-NAV returns.
6 Source of misvaluation: ETF or NAV?
In this section I provide more direct evidence that ETF premiums are driven by misvaluation in
the ETF leg (non-fundamental demand shocks) as opposed to in the NAV leg (slow diffusion of
information). To illustrate the testable implications, let us assume that the ETF i is hit by a
positive non-fundamental demand shock that pushes its price above the underlying portfolio
NAV value (ππ,π‘πΈβπ > 0). If ππ,π‘
πΈβπ truly reflects misvaluation of the ETF, then we should observe a
reversal in the future returns of ETF i (π π,π‘+1πΈππΉ < 0) with no impact on NAV returns (π π,π‘+1
ππ΄π = 0).
The alternative hypothesis is that the initial demand shock was driven by positive
fundamental news. In this case ETF i is correctly valued because the fundamental information is
incorporated first into ETF prices, while its underlying portfolio NAV is incorrectly priced
because it reacts more slowly, either because the high liquidity of ETFs attract fundamental
traders, or due to stale pricing. The difference from before is that the price is correct for ETF i
and its future returns remain unaffected (π π,π‘+1πΈππΉ = 0). In contrast, future NAV returns will be
21
positive as the NAV catches up to reflect the fundamental news already incorporated in the price
of ETF i (π π,π‘+1ππ΄π > 0). To test these implications, I estimate the following regressions while
controlling for lagged returns:
3 3
, 1 , 10 0
ETF ETF ETF E N ETF ETF ETF
i t i k t k k t k i tk kR a b P c R e
(7)
3 3
, 1 , 10 0
NAV NAV NAV E N NAV NAV NAV
i t i k t k k t k i tk kR a b P c R e
(8)
where π π,π‘+1πΈππΉ
= ETF return measured on day t (over two consecutive trading days)
π π,π‘+1ππ΄π
= NAV return measured on day t
ππ‘πΈβπ
= ETF premium relative to NAV on day t
If ππ,π‘πΈβπ reflects misvaluation for ETF i, then a future reversal in misvaluation implies that
πππΈππΉ < 0, while NAV returns remain unaffected ππ
ππ΄π = 0. In contrast, the information diffusion
story predicts that ππ,π‘πΈβπ reflects fundamental news already incorporated into the price of ETF i
(πππΈππΉ = 0), but future returns of NAV will catch up with a lag (ππ
ππ΄π > 0). I also report the
signifiance of the overall effect over a four day period (β ππ = 0) using an F-test.
The main challenge in estimating regressions (7) and (8) is the dependence in residuals
across funds because we have not accounted for common fundamental risk. To address this issue,
I estimate (7) and (8) using pooled OLS with Driscoll and Kraay (1998) standard errors that are
robust to general forms of cross-sectional and time-series dependence. In unreported tests, I also
very that similar results hold if we aggregate (7) and (8) to the style level by taking an equally-
weighted average of the LHS and RHS across all style categories (9 size-valuation styles for
non-sector ETFs, 11 sector styles).
[Table 6]
Consistent with the reversal of non-fundamental demand shocks, the results in Table 6 show that
premiums predict ETF returns negatively over a four day period with the overall effect being
significant at the 5 percent level. Individually, the coefficients are negative for the first three
lags, but significant only for the first two. The economic magnitude of the effect can be
illustrated by using a one Std. Dev. shock to premiums: the overall effect
(β ππ β ππ‘π. π·ππ£. (ππ,π‘πΈβπ)) equals a decline in ETF returns of 19.5 bps over a four day period.
The magnitude of this effect is considerable when compared to the overall variability in changes
22
in ETF misvaluation, which is 12 bps per day. In contrast, the overall effect of premiums on
NAV returns over a four day period is insignificantly different from zero.
These results might also be affected by arbitrage activity, namely, from the price impact of
buying the underpriced NAV and selling the overpriced ETF. In order to provide a more
conservative test I investigate the net effect of premiums on future ETF returns relative to NAV
returns (πππΈππΉ β ππ
ππ΄π). If premiums reflect non-fundamental demand shocks in ETF prices that
subsequently revert, then πππΈππΉ β ππ
ππ΄π < 0, whereas if premiums reflect fundamental demand
shocks in ETF prices and which are subsequently incorporated into NAV prices, then πππΈππΉ β
ππππ΄π > 0 . Surprisingly, the overall net effect (β(ππ
πΈππΉ β ππππ΄π) β ππ‘π. π·ππ£. (ππ,π‘
πΈβπ)) is even
more negative than before, at -30.1 bps, because premiums predict NAV returns with a negative
sign on days two and three.
This finding is in contradiction with the information diffusion story predicts, but it can be
explained in the context of non-fundamental demand shocks. Suppose investors trade
sequentially, possibly because information (whether fundamental or non-fundamental) arrives
sequentially. In this case, a positive non-fundamental demand shocks goes first to the most liquid
ETFs. Once liquidity dries up in the most liquid ETF, it goes to the next most liquid and so on,
until no more ETFs are liquid enough relative to their underlying basket, in which case the
demand goes to the underlying securities20
. Thus, a positive premium reflects misvaluation in
both the ETF and the NAV because both are hit by the demand shock, but the ETF is hit harder
because it is more liquid. Consequently, both ETF and NAV prices are above their true
fundamental values, in which case the returns of both must revert.
I also estimate regression (7) and (8) on sub-samples based on non-sector vs. sector, and
for large-, mid- and small-cap funds. The results hold strongly for both non-sector and sector
funds, although among the non-sector funds, only small-cap ETFs show significant evidence of
return reversals following a positive premium. This finding is not only consistent with non-
fundamental demand, but it also agrees with the conjecture that more liquid securities attract
short-term investors with non-fundamental demand because small-cap ETFs have on average
higher relative liquidity compared to either mid- or large-cap ETFs (Broman and Shum, 2015).
20
An alternative explanation is that liquidity demand by retail investors goes first to the most liquid ETF, then to the
next most liquid, and all the way to the least liquid ETF, because trading in the underlying securities is always too
costly. For institutional investors with the capacity to invest in the underlying securities, the demand would go to
ETFs only as long as ETF liquidity is above the liquidity of the underlying securities.
23
7 Correlated demand and excess comovement in returns
The non-fundamentals-based view of excess comovement predicts that if the degree of
commonality in demand shocks varies across securities or over time, then this variation should
be positively related to the degree of commonality in misvaluation and the liquidity of the fund
(Hypothesis 3). In order to test this hypothesis, we need empirical proxies for correlated demand
shocks. In section 7.1, I propose two such measures. In section 7.2 I show that these demand
shock proxies exhibit similar style-based comovements as do changes in ETF misvaluation. In
section 7.3, I provide formal tests for Hypothesis 3.
7.1 Measuring correlated demand shocks
To arrive at a proxy for abnormal demand shocks21
, I build on the concept of abnormal trading
activity. In the context of portfolio theory, turnover is a natural proxy for trading activity (Lo and
Wang, 2000). Hence, I use the turnover of an ETF relative to its underlying basket of securities:
, , , ,,1
ln /K
ETF UNDi t i k t k ti t
k
REL TO TO w TO
(9)
where: πππ,π‘πΈππΉ = πππΏπ,π‘
πΈππΉ/ππ»π π,π‘πΈππΉ, or the share volume divided by the number of shares
outstanding for ETF i on day t.
πππ,π‘πππ· = turnover of underlying security k on day t.
π€π,π,π‘ = dollar-weight invested by ETF i in security k at the end of day t
Lo and Wang (2000) use a similar measure of portfolio turnover. Higher numbers for REL(TO)
indicate that the ETF is more actively traded relative to its underlying basket, presumably
because the ETF attracts high-turnover investors. To arrive at a measure for unexpected shocks
to relative turnover, I use the residual from an AR(1) model, which I denote by βπ πΈπΏ(ππ).
Unexpected increases in βπ πΈπΏ(ππ) may reflect either an unexpected increase in ETF, or NAV
trading activity. The shocks are, however, most likely to come from the ETF rather than the
NAV because the correlation between βπ πΈπΏ(ππ) and a similarly constructed measure for shocks
to ETF turnover is roughly 0.9 (see also Broman and Shum (2015), Table 2).
21
Here I do not attempt to differentiate between the various sources (i.e. sentiment, risk aversion, or liquidity needs)
24
To investigate commonality in relative turnover, I adopt the same approach that I used for
ETF-NAV returns. Specifically, I regress shocks to relative trading activity on the equally-
weighted shock to relative trading activity of other funds in ETF i's own or distant styles (as
defined in the previous section):
1
, , , , ,, , ,1
i i j O i j DI i ti t OWN t j DIST t jj
REL TO REL TO REL TO u
(10)
The one-day leading and lagged terms are meant capture any lagged adjustment in commonality
(Chordia, Roll and Subrahmanyam, 2000). Correlated demand at the style level implies positive
concurrent own-style betas (π½π,π). One caveat is that I cannot rule out comovements across styles
(π½π,π·πΌ > 0) because βπ πΈπΏ(ππ) may also capture fundamental demand shocks. Nevertheless, I
would expect to find stronger own- than distant-style comovements if the non-fundamental style
component is strong.
As another measure of correlated demand, I use the degree of commonality in relative
liquidity. There is an extensive literature documenting that liquidity comoves across stocks. The
demand-side view argues that commonality in liquidity arises because of correlated trading
activity (Chordia, Roll and Subrahmanyam, 2000; Karolyi, Lee and Van Dijk, 2012), demand by
institutional owners (Kamara, Lou and Sadka, 2008), by investor sentiment (Huberman and
Halka, 2001) or by the price impact of correlated liquidity needs (Greenwood and Thesmar,
2011). In this case we can view commonality in ETF liquidity as a proxy for correlated demand.
The supply-side view provides a different interpretation. In this case liquidity commonality is
explained by the funding constraints of financial intermediaries. Several theoretical models
predict that commonality in liquidity, via illiquidity spirals or feedback loops, increases during
periods when arbitrage capital is limited22
. However, as we shall see in section 7.2, the results are
more consistent with the demand-side view of liquidity commonality.
To measure relative liquidity, I use the difference between the (log of) Amihudβs price
impact23
for the underlying portfolio and the ETF:
22
see Karolyi, Lee and Van Dijk (2012) for an extensive list of references. 23
Daily observations of the price impact ratio above the 99.5th
percentile of the sample have been discarded as in
Amihud (2002). Similar results obtain if I use the CRSP-based quoted spreads to measure liquidity.
25
, ,
, ,,1 , ,
log /
UND ETFK
k t i t
i k t UND ETFi tk k t i t
R RREL PI w
DVOL DVOL
(11)
where π π,π‘πππ· = mid-quite return (in %) for security k held by ETF i, on trading day t
π·πππΏπ,π‘πππ· = dollar volume (in $millions) for security k, on trading day t
Amihudβs Price Impact (PI) has been widely used in the literature. Hasbrouck (2009) reports
that, βamong the daily proxies, the Amihud measure is most strongly correlated with the TAQ-
based price impact coefficientβ (p. 1459). Amihudβs measure is also endorsed by several other
papers as good proxy for price impact; others have used it to study commonality in liquidity24
. A
similar measure of portfolio liquidity has been used by Idzorek, Xiong and Ibbotson (2012) and
Broman and Shum (2015). Having defined REL(PI), parallel calculations are done to compute
measures of commonality with REL(TO) replaced by REL(PI) in Eq. (10). The data for portfolio
weights comes from Morningstar Direct25
. For a more detailed description and summary
statistics of these variables, see Broman and Shum (2015).
According to the non-fundamentals based view of excess comovement there is a positive
relationship between the degree of commonality in misvaluation and turnover/liquidity because
both are driven by a common factor, namely correlated demand shocks. It is important to
emphasize that this prediction does not imply that ETF-NAV returns can be explained by relative
turnover/liquidity (or by the own-style turnover/liquidity factors). In particular, commonality in
turnover/liquidity tends to be high during market downturns when volatility is high and when
returns are extremely low (Karolyi, Lee and Van Dijk, 2012), while liquidity is high in the
opposite state and turnover can be high in either extreme state.
The theoretical model by Cherkes, Sagi and Stanton (2008) does, however, predict a
positive relationship between the return difference of twin securities and their liquidity difference
because premiums reflect a trade-off between liquidity and expense ratios. Their prediction can
explain the style-based commonality in misvaluation documented previously only if changes in
relative liquidity are correlated across ETFs at the style level, and if such common changes in
liquidity can explain ETF-NAV return differences. In unreported tests, I investigate this issue by
24
Lesmond (2005), Goyenko, Holden and Trzcinka (2009), Fong, Holden, and Trzcinka (2010) endorse Amihud,
while Karolyi, Lee and Van Dijk (2012) and Kamara, Lou and Sadka (2008) use Amihud for liquidity commonality. 25
Since my holdings data for the underlying holdings of an ETF is generally at the monthly level, the implicit
assumption is that changes in weights only reflect changes in market values of the constituents.
26
regressing changes in premiums (i.e. ETF-NAV returns) on shocks to relative turnover and
relative liquidity (Eq. (9) and (11)) and the own- and distant-style factors for turnover/liquidity.
The liquidity measures are consistently insignificant.
7.2 Results: commonality in demand shocks
Table 7 presents the results for correlated demand shocks, as estimated from Eq. (10) for shocks
to relative turnover (Panel A), or relative liquidity (Panel B). I report the following results:
average and median values for the concurrent, lagged, lead, sum coefficients and R2; the
percentage of funds with positive coefficients, the percentage of funds with positive and
significant coefficients, negative and significant coefficients. Test of statistical significance for
the average (median) coefficient is based on the cross-sectional t-statistic (sign-test) similar to
Chordia, Roll and Subrahmanyam (2000) and Brockman et al. (2009). The results show that
shocks to relative turnover βπ πΈπΏ(ππ) comove positively and significantly across ETFs in the
same style both at the mean and the median. More than 93 percent of the concurrent own-style
betas (π½π,π) are positive and (individually) significant at least at the 5 % level. Although shocks
to relative trading activity also comove across distant styles (π½π,π·πΌ > 0), the magnitude of the
distant-style betas are less than a third as large as the own-style betas.
[Table 7]
The results for relative liquidity are even stronger: shocks to relative liquidity exhibit
positive and significant own-style comovements (in 99 percent of cases), while the distant-style
comovements are significantly negative (π½π,π·πΌ < 0). This is consistent with the earlier results for
commonality in misvaluation and with the prediction by Barberis and Shleifer (2003) that
increases in own-style allocations are at least partly financed by decreases in distant-style
allocations. Moreover, these style-based comovements in turnover and liquidity are more
consistent with demand than supply-side explanations given that the theoretical effects behind
the latter (illiquidity spirals and feedback loops) are generally described as a market-wide
phenomenon.
Overall, the results in this section highlight that proxies for demand shocks (relative
turnover and price impact) exhibit similar style-based comovements as do ETF-NAV returns.
Similar results are also obtained when turnover/liquidity shocks are measured at the ETF level
27
(ETF turnover or price impact instead of relative turnover or relative price impact), suggesting
that commonality in demand shocks is mainly coming from the ETF, rather than the NAV leg.
7.3 Explaining the amount of commonality in misvaluation
Hypothesis 3 predicts a link between the degree of commonality in misvaluation, commonality in
demand shocks and the level of fund liquidity. In this context, what is the appropriate measure of
the degree of commonality? The existing literature mainly uses the regression R2 (e.g. Morck,
Yeung and Yu, 2000; Hameed, Kang and Viswanathan, 2010; Karolyi, Lee and Van Dijk, 2012),
although the beta coefficient is also used (Kamara, Lou and Sadka, 2008).
I use the R2 measure for three reasons. First, the beta is sensitive to scaling effects that arise
from differences in factors and their volatilities (i.e. the beta denominator) across ETF styles.
Second, it is difficult to make cross-sectional comparisons of betas in short samples due to large
cross-sectional differences in the Std. Dev. of ETF-NAV returns, which is also directly related to
arbitrage costs (funds with higher arbitrage costs have more volatile ETF-NAV returns). The R2-
measure does not suffer from these problems as it is a function of both the variance of the
dependent variable and the factors. Another interpretation of the R2-measure is that it captures
the proportion of common vs. idiosyncratic risk, in which case it is not sensitive to total
misvaluation. This metric is also suitable for testing the hypothesis that commonality in
misvaluation is stronger for more liquid ETFs. In unreported robustness tests I verify that the
main results continue to hold for beta coefficients.
The regression R2 (labelled π πππ‘,π
2 ) from Eq. (4) is estimated every month m on daily data.
I require at least 15 non-missing observations per month. Since regression (4) also controls for
the lagged premium, I decompose the model R2 as:
, , 1 , , , ,, ,
, , ,
, , ,2E N E N E N E N E N E N
ii t i t i t OWN t i t DI ti OWN i DI
E N E N E Ni t i t i t
COV R P COV R R COV R R
mVAR R VAR R VAR R
R
(12)
and use the sum of the last two normalized covariance terms, denoted π πππ‘,π2 , to measure the
degree of commonality in misvaluation. π πππ‘,π2 can be interpreted as the fraction of the model R
2
attributable to the own- and distant-style factors (Graham, Li and Qiu, 2013). Similarly, I
measure commonality in relative turnover/liquidity shocks from the fraction of model R2
28
attributable to the concurrent own and distant-style factors from Eq. (10). The degree of
commonality in relative turnover and price impact is denoted by π πππ,π2 and π πππΌ,π
2 respectively.
To investigate the relationship between commonality in misvaluation, commonality in
demand shocks and liquidity, I estimate the following regression using pooled OLS:
2 2
, 1 , 1 2 , 1 3 , 1 4 ,ret m dem m i m i m m i mR a b R b LIQ b Fund b Macro FE e (13)
where π πππ,πβ12 = commonality in demand shocks based on π πππ,π
2 or π πππΌ,π2
πΏπΌππ,π‘β1 = ETF & underlying portfolio liquidity during month t-1
πΉπ’πππ,πβ1 = vector of fund characteristics
ππππππ = vector of macro variables
πΉπΈ = fixed effects: year, month, sector, style and/or fund
As a direct and salient measure of liquidity, I use the monthly average quoted spread for ETF i:
, ,,
1 , ,
11*ln 100*
/ 2
mETF ETFNi t i tETF
i m ETF ETFm t i t i t
ASK BIDQSPR
N ASK BID
(14)
where: π΄ππΎπ,π‘πΈππΉand π΅πΌπ·π,π‘
πΈππΉ = CRSP ask and bid price at the close on trading day t for ETF i
Nm = nr. of trading days in calendar month m
I use the log-transformation to mitigate the impact of outliers and to deal with the apparent non-
stationarity in the data. I estimate the portfolio quoted spread by dollar-weighting the monthly
quoted spread of each security included in the ETFβs basket ( ππππ π,ππππ· = π€π,π,πππππ π,π
πππ· ).
According to Chung and Zhang (2014), the CRSP-based spread is highly correlated with the
(more accurate) TAQ spread in the cross-section, which is the dimension of primary interest. I
also include the expense ratio because it is a salient cost for retail investors (Grinblatt et al.,
2014). Another implicit measure of liquidity is total misvaluation, measured by the absolute
value of the monthly average premium (Eq. (2)), because funds with high misvaluation have high
arbitrage costs.
Arbitrage activity should be negatively related to the degree of commonality in
misvaluation because it is associated with greater pricing efficiency. To measure arbitrage
activity, I use share creation/redemption activity, defined as in Broman and Shum (2015):
29
, , 1
,
1 , 1
1log 1
Nmi d i d
i m
dm i d
SHR SHRCREATE
N SHR
(15)
where: ππ»π π,π = shares outstanding for ETF i on day d;
Nt = number of trading days in calendar month t.
Commonality in misvaluation should be greater when market-wide arbitrage costs are high
because they leave more βroomβ for excess comovement (Kumar and Lee, 2006; Kumar and
Spalt, 2013). I use the funding liquidity factor by Hu, Pan and Wang (2013), which is based on
price deviations between on-the-run and off-the-run Treasury securities, averaged across a wide
range of maturities. Market volatility is also an important determinant of the risk to market
makers of maintaining inventories of their securities (Chordia, Roll, and Subrahmanyam, 2000),
and changes in market volatility can cause changes in inventories and create correlated
institutional trading. Market volatility is also related aggregate uncertainty in financial markets
either via higher transaction costs or lower funding liquidity (i.e., less capital is devoted to ETF
arbitrage) as in Brunnermeier and Pedersen (2009). In either case, the prediction is that
commonality in misvaluation should be positively related to market volatility, which I proxy for
by the Std. Dev. of NAV returns.
[Figure 1]
Before I discuss the regression results, I illustrate the time-series dynamics for the cross-
sectional mean degree of commonality in misvaluation (π πππ‘,π2 ) in Figure 1. Panel A depicts
π πππ‘,π2 across three terciles based on the degree of commonality in relative liquidity (via price
impact) in the prior month (π πππΌ,πβ12 ), while in Panel B, I instead use three terciles based on
relative quoted spreads (ππππ π,πβ1πΈππΉ β ππππ π,πβ1
πππ· ). We can see that ETFs in the top tercile of
commonality in relative price impact have a higher degree of commonality in misvaluation in 99
% of quarters (93 % are significant at the 5 % level) relative to ETFs in the lowest tercile.
Moreover, ETFs in the highest tercile of relative quoted spreads have stronger commonality in
misvaluation in 98 % of the quarters (70 % are significant at the 5 % level). These preliminary
findings agree with the conjecture that commonality in misvaluation is higher when commonality
in demand shocks is high, and for ETFs with more desirable liquidity characteristics.
[Table 8]
30
The results in Table 8 show that commonality in misvaluation is positively and
significantly related to commonality in demand shocks (via π πππ2 and π πππΌ
2 ). When both measures
for commonality in demand shocks are included simulatenously, π πππΌ2 remains highly significant
while π πππ2 is only marginally significant. This is not surprising because the two measures are
designed to capture the same thing. Moreover, commonality in misvaluation is significantly
higher for more liquid ETFs (lower quoted spreads, expense ratios and total misvaluation), for
less liquid underlying portfolios, and during times when arbitrage is limited (high market
volatility, low funding liquidity). Similar results are obtained in sub-samples of non-sector vs.
sector funds, or if we control for time or ETF fixed effects in addition to style fixed effects.
Overall, the findings in this section show that the degree of commonality in misvaluation is
stronger for ETFs with more correlated demand shocks and more desirable liquidity
characteristics, which supports my conjecture that excess comovements in ETF returns are
driven by correlated non-fundamental demand and facilitated by investors with short horizons
that are attracted to ETFs because of their high liquidity.
8 Summary and Conclusions
This study analyzes whether the returns of Exchange Traded Funds (ETFs) comove excessively
with other ETFs in similar investment styles. My conjecture is that, due to the ease of investing
in ETFs and because of their high liquidity, ETFs attract a clientele of short-term investors who
are more exposed to common non-fundamental demand shocks at the style level relative to the
investor in the ETFs underlying baskets.
In order to identify excess comovements, I look for common factors in changes in
misvaluation (ETF-NAV returns); in order to attribute this misvaluation to the ETF leg, I study
return reversals following shocks to misvaluation; and in order to link the degree of excess
comovement to common non-fundamental demand shocks and to liquidity clientele differences, I
investigate how the degree of commonality in misvaluation is related to the degree of
commonality in turnover/liquidity (proxy for demand shocks) and ETF characteristics that are
attractive to investors with short-term trading needs.
My findings indicate that there is significant style-based commonality in misvaluation:
changes in misvaluation comove positively across ETFs in similar styles, and negatively with
ETFs in distant styles. Although the importance of common misvaluation is found to persist
31
across daily, weekly and monthly horizons, the economic magnitude of these shocks declines
with the return horizon consistent with arbitrage. The source of misvaluation is found to be the
ETF since current ETF premiums negatively predict future ETF returns consistent with
temporary demand shocks in the ETF prices. Such reversals are strongest for small-cap ETFs,
which is consistent with the conjecture that more liquid securities (small-cap ETFs have the
highest relative liquidity) attract short-term investors with non-fundamental demand.
Moreover, shocks to the abnormal trading activity of ETFs and to the liquidity of ETFs
(both relative to their underlying baskets) exhibit similar style-based commonality. These proxies
for correlated demand shocks also predict the future amount of commonality in ETF
misvaluation. In accordance with liquidity being a factor in inducing clientele differences
between ETFs and their underlying portfolio, I show that the degree of commonality in
misvaluation is higher among ETFs more desirable liquidity characteristics.
My overall conclusion is that the excess comovement in ETF returns is mainly driven by
the correlated non-fundamental demand of a liquidity-based clientele. Thus, more liquid
securities may encourage trading for reasons unrelated to fundamentals, which can at times be
detrimental for pricing efficiency.
References
Aggarwal, R. and Schofield, L. (2012): The Growth of Global ETFs and Regulatory Challenges. Available at
SSRN: http://ssrn.com/abstract=2001060 or http://dx.doi.org/10.2139/ssrn.2001060
Amihud, Y., & Mendelson, H. (1986). Asset pricing and the bid-ask spread. Journal of financial Economics, 17(2),
223-249.
Amihud, Y. (2002). Illiquidity and stock returns: cross-section and time-series effects. Journal of financial markets,
5(1), 31-56.
Anton, M., & Polk, C. (2014). Connected stocks. The Journal of Finance, 69 (3), pp. 1099-1127.
Baker, M., & Wurgler, J. (2006). Investor Sentiment and the Cross-Section of Stock Returns. The Journal of
Finance, 61(4), 1645-1680.
Banz, R. W. (1981). The relationship between return and market value of common stocks. Journal of financial
economics, 9(1), 3-18.
Barber, B. M., Odean, T., & Zhu, N. (2009). Do retail trades move markets?. Review of Financial Studies, 22(1),
151-186.
Barberis, N., & Shleifer, A. (2003). Style investing. Journal of Financial Economics, 68(2), 161-199.
Barberis, N., Shleifer, A., & Wurgler, J. (2005). Comovement. Journal of Financial Economics, 75(2), 283-317.
32
Barberis, N., & Thaler, R. (2003). A survey of behavioral finance. Handbook of the Economics of Finance, 1, 1053-
1128.
Ben-David, I., Franzoni, F., and Moussawi, R. (2014): Do ETFs Increase Volatility? Available at SSRN:
http://ssrn.com/abstract=1967599.
Ben-Rephael, A., Kadan, O., and Wohl, A. (2013): The Diminishing Liquidity Premium. Journal of Financial and
Quantitative Analysis, Forthcoming.
Blackrock (2012): ETP Landscape, Global handbook 2012. Availble at:
http://www.blackrockinternational.com/intermediaries/en-fi/insights/etp-landscape
Bodurtha, J.N., Kim, D-S., Lee, C.M.C (1995): Closed-end Country Funds and U.S. Market Sentiment, The Review
of Financial Studies, Vol. 8, No. 3, pp. 879-918.
Brav, A., Heaton, J. B., & Li, S. (2010). The limits of the limits of arbitrage. Review of Finance, 14(1), 157-187.
Brockman, P., Chung, D. Y., & PΓ©rignon, C. (2009). Commonality in liquidity: A global perspective. Journal of
Financial and Quantitative Analysis, 44(04), 851-882.
Brown, S. J., & Goetzmann, W. N. (1997). Mutual fund styles. Journal of financial Economics, 43(3), 373-399.
Broman, M. and Shum, P. (2015): Short-Term Trading and Liquidity Clienteles: Evidence from Exchange-Traded
Funds. Available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2361514
Campbell, J. Y., Polk, C., & Vuolteenaho, T. (2010). Growth or glamour? Fundamentals and systematic risk in stock
returns. Review of Financial Studies, 23(1), 305-344.
Campbell, J. Y., Giglio, S., Polk, C., & Turley, R. (2013). An Intertemporal CAPM with Stochastic Volatility (No.
w18411). National Bureau of Economic Research.
Chan, L. K., Chen, H. L., & Lakonishok, J. (2002). On mutual fund investment styles. Review of financial studies,
15(5), 1407-1437.
Chan, J. S., Hong, D., & Subrahmanyam, M. G. (2008). A tale of two prices: Liquidity and asset prices in multiple
markets. Journal of Banking & Finance, 32(6), 947-960.
Cherkes, M., Sagi, J., & Stanton, R. (2009). A liquidity-based theory of closed-end funds. Review of Financial
Studies, 22(1), 257-297.
Chordia, T., Roll, R., & Subrahmanyam, A. (2000). Commonality in liquidity. Journal of Financial Economics,
56(1), 3-28.
Cooper, M. J., Gulen, H., & Rau, P. R. (2005). Changing names with style: Mutual fund name changes and their
effects on fund flows. The Journal of Finance, 60(6), 2825-2858.
Da, Z., & Shive, S. (2013). When the Bellwether Dances to Noise: Evidence from Exchange-Traded Funds.
Available at SSRN: http://ssrn.com/abstract=2158361.
DeLisle, Jared and French, Dan W. and Schutte, Maria G. (2013): What Does Rising Comovement Mean for Price
Informativeness? An Examination of Average R2 Trends). Available at SSRN:
http://ssrn.com/abstract=2166118
DeLong, J. B., Shleifer, A., Summers, L.H. and Waldmann, R. (1990): Noise trader risk in financial markets.
Journal of Political Economy, 98(4):703-738.
Driscoll, John C., and Aart C. Kraay (1998): Consistent covariance matrix estimation with spatially dependent panel
data, Review of Economics and Statistics 80, pp. 549β560.
33
Engle, R. and Sarkar, D. (2006): Premiums-Discounts and Exchange Traded Funds. The Journal of Derivatives,
2006 (1), pp. 27-45.
Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of
Financial Economics 33, 3β56.
Fama, Eugene F., and Kenneth R. French, 1995, Size and book-to-market factors in earnings and returns, Journal of
Finance, 50, 131β155.
Frazzini, A., & Lamont, O. A. (2008). Dumb money: Mutual fund flows and the cross-section of stock returns.
Journal of Financial Economics, 88(2), 299-322.
Fong, K., Holden, C.W., Trzcinka, C.A. (2010): Can global stock liquidity be measured? Unpublished working
paper. University of New South Wales and Indiana University.
Froot, K., & Teo, M. (2008). Style investing and institutional investors. Journal of Financial and Quantitative
Analysis, 43(4), 883.
Gagnon, L., & Andrew Karolyi, G. (2010). Multi-market trading and arbitrage. Journal of Financial Economics,
97(1), 53-80.
Graham, J. R., Li, S., & Qiu, J. (2012). Managerial attributes and executive compensation. Review of Financial
Studies, 25(1), 144-186.
Green, T. C., & Hwang, B. H. (2009). Price-based return comovement. Journal of Financial Economics, 93(1), 37-
50.
Greenwich Associates (2013): Institutional Investors Relation with ETFs deepen. Available at:
http://us.ishares.com/content/en_us/repository/resource/greenwich_survey_inst.pdf
Greenwood, R. (2007): Excess comovement of stock returns: Evidence from cross-sectional variation in Nikkei 225
weights. Review of Financial Studies, 21.3, pp. 1153-1186.
Greenwood, R., & Thesmar, D. (2011). Stock price fragility. Journal of Financial Economics, 102(3), 471-490.
Goyenko, R. Y., Holden, C. W., & Trzcinka, C. A. (2009). Do liquidity measures measure liquidity? Journal of
Financial Economics, 92(2), 153-181.
Hardouvelis, G., Porta, R. L., & Wizman, T. A. (1994). What moves the discount on country equity funds?. In The
internationalization of equity markets (pp. 345-403). University of Chicago Press.
Hameed, A., Kang, W., & Viswanathan, S. (2010). Stock market declines and liquidity. The Journal of Finance,
65(1), 257-293.
Hasbrouck, J. (2009). Trading costs and returns for US equities: Estimating effective costs from daily data. The
Journal of Finance, 64(3), 1445-1477.
Huang, M. (2003). Liquidity shocks and equilibrium liquidity premia. Journal of Economic Theory, 109(1), 104-
129.
Hu, G. X., Pan, J., & Wang, J. (2013). Noise as information for illiquidity. The Journal of Finance, 68(6), 2341-
2382.
Huberman, G., Halka, D. (2001): Systematic liquidity. Journal of Financial Research, 24,pp. 161β178.
Idzorek, T. M, Xiong, J. X. and Ibbotson, R. G. (2012). The Liquidity Style of Mutual Funds. Financial Analyst
Journal, 68 (6),
34
Kamara, A., Lou, X., & Sadka, R. (2008). The divergence of liquidity commonality in the cross-section of stocks.
Journal of Financial Economics, 89(3), 444-466.
Karolyi, G. A., Lee, K. H., & Van Dijk, M. A. (2012). Understanding commonality in liquidity around the world.
Journal of Financial Economics, 105(1), 82-112.
Kasch, M., & Sarkar, A. (2012). Is there an S&P 500 Index effect?. Available at SSRN 2171235.
Korajczyk, R. A., & Sadka, R. (2008). Pricing the commonality across alternative measures of liquidity. Journal of
Financial Economics, 87(1), 45-72.
Kumar, A., & Lee, C. (2006). Retail investor sentiment and return comovements. The Journal of Finance, 61(5),
2451-2486.
Kumar, A. (2009). Dynamic style preferences of individual investors and stock returns. Journal of Financial and
Quantitative Analysis, 44(03), 607-640.
Kumar, A., Page, J. K., & Spalt, O. G. (2013). Investor Sentiment and Return Comovements: Evidence from Stock
Splits and Headquarters Changes. Review of Finance, 17(3), 921-953.
Kumar, A., Page, J. K., & Spalt, O. G. (2013b): Gambling and Comovement. Journal of Financial and Quantitative
Analysis, forthcoming.
Lee, C.M., Shleifer, A. and Thaler, R.H. (1991): Investor Sentiment and the Closed-End Fund Puzzle. The Journal
of Finance, XLVI (1), pp. 75-109.
Lesmond, D. (2005): Liquidity of emerging markets. Journal of Financial Economics, 77, 411β452.
Lo, A. W., & Wang, J. (2000). Trading volume: definitions, data analysis, and implications of portfolio theory.
Review of Financial Studies, 13(2), 257-300.
Lo, A., W., Mamaysky, H., & Wang, J. (2004). Asset Prices and Trading Volume under Fixed Transactions Costs.
Journal of Political Economy, 112(5).
Lynch, A. W., & Tan, S. (2011). Explaining the Magnitude of Liquidity Premia: The Roles of Return Predictability,
Wealth Shocks, and State-Dependent Transaction Costs. The Journal of Finance, 66(4), 1329-1368.
Marshall, B. R., Nguyen, N. H., & Visaltanachoti, N. (2013). ETF arbitrage: Intraday Evidence. Journal of Banking
and Finance, 37(9), 3486-3498.
Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometrica: Journal of the Econometric
Society, 867-887.
Morck, R., Yeung, B., & Yu, W. (2000): The information content of stock markets: why do emerging markets have
synchronous stock price movements?. Journal of financial economics, 58(1), 215-260.
Perez, F., Shkilko, A., & Tang, T. (2011): Signaling Via Stock Splits: Evidence from Short Interest. In AFA 2012
Chicago Meetings Paper.
Petajisto, A (2013): Inefficiencies in the Pricing of Exchange-Traded Funds. Available at SSRN:
http://ssrn.com/abstract=2000336 or http://dx.doi.org/10.2139/ssrn.1572907
Pontiff, J. (2006). Costly arbitrage and the myth of idiosyncratic risk. Journal of Accounting and Economics, 42(1),
35-52.
Pirinsky, C., & Wang, Q. (2006). Does corporate headquarters location matter for stock returns? The Journal of
Finance, 61(4), 1991-2015.
35
Richie, Nivine, Robert Daigler, and Kimberly C. Gleason (2008): The limits to stock index arbitrage: Examining
S&P 500 futures and SPDRs, Journal of Futures Markets, 28(12), 1182β 1205.
Rinne, K., Suominen, M., & Vaittinen, L. (2014). Dash for Cash: Month-End Liquidity Needs and the Predictability
of Stock Returns. Available at SSRN.
Staer, A. (2014). Fund Flows and Underlying Returns: The Case of ETFs. Available at SSRN 2158468.
Teo, M., & Woo, S. J. (2004). Style effects in the cross-section of stock returns. Journal of Financial Economics,
74(2), 367-398.
Wurgler, Jeffrey (2010): On the Economic Consequences of Index-Linked Investing, National Bureau of Economic
Research Working Paper Series No. 16376.
Yan, X. S. (2008). Liquidity, investment style, and the relation between fund size and fund performance. Journal of
Financial and Quantitative Analysis, 43(03), 741-767.
36
Figure 1: Commonality in misvaluation, commonality in demand shocks and the level of liquidity
The cross-sectional mean degree of commonality in misvaluation is plotted over time for three groups. Terciles are
based on commonality in relative price impact (π ππππ,πβ12 ) and the level of relative quoted spreads in Panels A and B
respectively. The degree of commonality is based on the model R2, or the fraction of the variation in the dependent
variable (ETF-NAV returns, relative turnover or liquidity) attributable to the own and distant style factors.
Panel A: Cross-sectional mean of πΉπππ,ππ by πΉππ·π°,πβπ
π tercile
Panel B: Cross-sectional mean of πΉπππ,ππ by πΉπ¬π³(π³π°πΈ) tercile
37
Table 1: Snapshot of ETF statistics
This table reports the number of ETFs and the total Assets under Management (AUM) at the beginning, the middle and at
the end of the sample. The statistics are reported by Morningstar 3-by-3 style classification (size and valuation) for ETFs
with a core style, and by Morningstar industry styles for sector ETFs.
Nr. of ETFs AUM (in $millions)
Category 01/2006 06/2009 12/2012 01/2006 06/2009 12/2012
Core styles 53 73 79 168,391 210,116 425,491
Large-Value 8 12 11 16,042 20,398 43,041
Large-Blend 12 16 21 81,368 105,540 220,168 Large-Growth 8 11 12 31,840 33,355 64,670
Mid-Value 3 5 5 4,589 4,020 7,373
Mid-Blend 4 6 6 6,906 16,174 34,492 Mid-Growth 4 5 5 4,008 4,404 7,854
Small-Value 5 4 3 5,228 4,178 6,661
Small-Blend 4 8 10 13,874 16,321 31,925
Small-Growth 5 6 6 4,537 5,727 9,307
Sector styles 42 83 85 31,438 47,428 114,520
Communication 2 2 2 551 650 936
Cons. Cyclical 3 7 7 759 3,158 9,348
Cons. Defens. 3 4 4 1,334 2,756 7,258
Energy 4 9 9 6,657 8,067 12,877
Financial 4 11 13 2,383 8,756 14,098
Real Estate 4 10 10 5,012 5,652 26,087
Health Care 4 11 11 5,216 5,448 11,498
Industrials 4 8 8 1,314 2,188 5,953
Materials 3 5 5 1,241 2,406 4,675
Technology 8 12 12 3,851 5,562 14,239 Utilities 3 4 4 3,120 2,788 7,552
All 95 156 164 199,829 257,545 540,011
38
Table 2: Descriptive Statistics
πππΈβπ (π π
πΈβπ) is the level of (change in) premium calculated as the log-price (return) difference the ETF price and the NAV
price. Both levels and changes in premiums are reported in percentage. Closing and mid-point refers to premiums
calculated using closing or mid-point prices/returns. Summary statistics are calculated using daily data, over the 01/2006 to
12/2012 period. Statistics are reported by Morningstarβs 3-by-3 style classification for funds with a core (non-sector) style,
and by Morningstar industry style for sector funds.
Variable Style Mean Median Std. Dev. 1 % 99 %
Closing: πππΈβπ = ππ(ππ
πΈππΉ/ππππ΄π) All funds -0.005 0.000 0.163 -0.553 0.522
Mid-point: πππΈβπ = ππ(ππ
πΈππΉ/ππππ΄π)
All funds -0.005 -0.003 0.091 -0.268 0.271
By size
Large -0.015 -0.013 0.115 -0.372 0.307
Mid -0.007 -0.007 0.083 -0.220 0.248
Small 0.001 0.000 0.080 -0.198 0.252
By valuation
Blend -0.003 0.000 0.088 -0.257 0.262
Value -0.004 0.000 0.092 -0.277 0.289
Growth -0.007 -0.007 0.093 -0.277 0.270
By core vs. sector
Core -0.005 -0.003 0.091 -0.268 0.271
Sector -0.005 -0.007 0.121 -0.302 0.361
Closing: π ππΈβπ = π π
πΈππΉ β π πππ΄π All funds 0.000 0.000 0.224 -0.730 0.710
Mid-point: π ππΈβπ = π π
πΈππΉ β π πππ΄π
All funds 0.000 0.000 0.120 -0.371 0.356
By size
Large 0.000 0.000 0.150 -0.457 0.444
Mid 0.000 0.000 0.119 -0.338 0.334
Small 0.000 0.000 0.103 -0.311 0.301
By valuation
Blend 0.000 0.000 0.113 -0.350 0.337
Value 0.000 0.000 0.121 -0.388 0.373
Growth 0.000 0.000 0.127 -0.383 0.371
By core vs. sector
Core 0.000 0.000 0.120 -0.371 0.356
Sector 0.000 0.000 0.169 -0.463 0.465
39
Table 3: Style-based commonality in misvaluation
This table reports results from estimating the following regression, fund-by-fund:
, , 1 , , , , , , ,
E N E N E N E N
i t i i i t i OWN OWN i t i DI DIST i t i tR P R R e
where π ππΈβπ is the ETF-NAV return difference (or equivalently the change in premium, βππ
πΈβπ) and πππΈβπis the ETF premium. π πππ
πΈβπ is the own-style mispricing factor,
which is based on the average ETF-NAV return of other ETFs in matching styles: equal weight is given to funds that match both style dimensions (size and valuation),
and half the equal weight to funds that are in adjacent styles (if ETF i is Large-Value, then adjacent styles include Mid-Value and Large-Blend). For ETFs belonging to
sector styles, equal weight is given to funds in the same industry, half the equal weight to funds in the same size and valuation category and one fourth of the equal weight
to funds in adjacent core styles. π π·πΌπππΈβπ is the distant-style mispricing factor and it is based on the average ETF-NAV return of other ETFs in opposite styles: equal weight
is given to funds that are in opposite styles (both size and valuation) and half the equal weight to funds that are in styles adjacent to the opposite style. For instance, if ETF
i is Large-Value, then Small-Growth is the opposite style (equal-weight) and Mid-Growth and Small-Blend (half the equal weight) are in styles adjacent to Small-Growth.
For mid-cap funds we consider large and small to be equally distant. Blend funds (neither value, nor growth) are matched only by their size category. Hence, the distant
style of Mid-Value is Small-Growth and Large-Growth. The t-statistic for the average coefficient is adjusted for cross-correlation as in Hameed, Kang and Viswanathan
(2010). Impact (basis points) is the impact of a 1 Std. Dev. increase in the RHS variable on the dependent variable, while impact [%πππ·(π π,π‘πΈβπ)] and impact
[%πππ·(π π,π‘πΈππΉ)] are the impact in basis points scaled by the Std. Dev. of the dependent variable and raw ETF return respectively. Coefficients and t-statistics are also
reported at the 5th, 50th and 95th percentile of the cross-sectional distribution. In this case the t-statistics are based on heteroskedasticity-robust standard errors. */**/***
denotes statistical significance at the 10, 5 and 1 %.
Daily horizon Weekly horizon Monthly horizon
ππ π½π,πππ π½π,π·πΌππ ππ π½π,πππ π½π,π·πΌππ ππ π½π,πππ π½π,π·πΌππ
Average coefficient -0.523*** 0.819*** -0.071*** -0.567*** 0.783*** -0.057 -0.580*** 0.737*** -0.025
(26.44) (26.65) (2.61) (14.59) (13.34) (1.13) (10.51) (8.46) (0.34)
Econonomic significance:
Impact [basis points]: -5.43 6.99 -0.63 -5.47 7.54 -0.55 -6.56 7.97 -0.26
Impact [%πππ·(π π,π‘πΈβπ)] -38.61 55.73 -3.72 -37.34 56.22 -4.38 -38.06 45.91 -0.39
Impact [%πππ·(π π,π‘πΈππΉ)] -2.94 4.01 -0.33 -1.56 2.29 -0.19 -1.01 1.27 -0.02
Distribution of coefficients:
5th percentile -0.848*** 0.314* -0.399*** -0.950*** 0.158 -0.531*** -1.119*** -0.210 -0.853***
(-14.48) (1.91) (-4.48) (-8.73) (0.68) (-3.15) (-7.27) (-0.36) (-2.97)
50th percentile -0.488*** 0.792*** -0.071 -0.560*** 0.783*** -0.050 -0.568*** 0.720*** -0.019
(-8.77) (9.54) (-1.00) (-4.50) (4.37) (-0.41) (-3.01) (2.76) (-0.08)
95th percentile -0.258*** 1.403*** 0.234*** -0.195 1.376*** 0.462*** -0.008 1.497*** 0.601***
(-3.96) (24.61) (2.92) (-1.48) (13.53) (2.22) (-0.03) (8.72) (2.41)
Average R2 0.64 0.67 0.62
N obs 260,451 53,764 13,664
40
Table 4: Sub-sample results for commonality in misvaluation
This table reports results from estimating the following regression on daily data, fund-by-fund:
, , 1 , , , , , , ,
E N E N E N E N
i t i i i t i OWN OWN i t i DI DIST i t i tR P R R e
where π ππΈβπ is the ETF-NAV return difference (or equivalently the change in premium, βππ
πΈβπ) and πππΈβπ is the ETF
premium. π ππππΈβπ is the own-style mispricing factor, which is based on the average ETF-NAV return of other ETFs in
matching styles. π π·πΌπππΈβπ is the distant-style mispricing factor and it is based on the average ETF-NAV return of other ETFs
in opposite styles. For further details on the construction of these factors and the own vs. distant style classification, see
Table 3. The beta coefficients reported are average betas across all funds in a given style. The t-statistic for the average
coefficient is adjusted for cross-correlation as in Hameed, Kang and Viswanathan (2010). Impact [%πππ·(π π,π‘πΈβπ)] = 100 β
π½πππ,π β πππ·(π ππππΈβπ )/πππ·(π π,π‘
πΈβπ) , or in words, the impact of a 1 Std. Dev. increase in the own-style factor as a
percentage of the Std. Dev. of the dependent variable. Similarly, Impact [%πππ·(π π,π‘πΈππΉ)] = 100 β π½πππ,π β πππ·(π πππ
πΈβπ )/
πππ·(π π,π‘πΈππΉ), or the impact of a 1 Std. Dev. increase in the own-style factor as a percentage of the Std. Dev. of raw ETF
returns. */**/*** denotes statistical significance at the 10, 5 and 1 %.
Sub-
sample π½π,πππ [t-stat]
Impact
[%πππ·(π π,π‘πΈβπ)]
Impact
[%πππ·(π π,π‘πΈππΉ)] π½π,π·πΌππ [t-stat] Avg. R2 N obs
All 0.819 [26.65] 55.73 4.01 -0.071 [2.61] 0.644 260,451
Diversified non-sector
Large 0.843 [37.82] 65.17 4.52 -0.039 [3.51] 0.702 66,255
Mid 0.828 [19.96] 65.22 3.84 -0.083 [2.19] 0.680 28,613
Small 0.957 [49.05] 68.39 5.50 -0.088 [2.86] 0.728 31,197
Blend 0.800 [42.76] 62.81 4.38 0.000 [1.32] 0.717 52,821
Value 1.037 [35.14] 75.56 5.54 -0.173 [6.86] 0.725 34,475
Growth 0.805 [32.09] 61.41 4.09 -0.071 [3.59] 0.665 38,769
Sector 0.774 [18.99] 46.22 3.44 -0.081 [2.13] 0.588 134,881
Time-period: 01/2002 to 12/2006
All 0.590 [8.60] 31.82 2.47 -0.028 [0.55] 0.553 65,003
Time-period: 12/2006 to 07/2008
All 0.724 [21.68] 47.16 3.54 -0.042 [1.51] 0.724 82,927
Time-period: 08/2008 to 03/2009
All 0.884 [15.62] 63.17 5.34 -0.102 [1.84] 0.673 25,300
Time-period: 03/2009 to 12/2012
All 0.799 [30.27] 54.94 3.04 -0.070 [3.37] 0.660 152,719
41
Table 5: Differences in systematic risk?
This table reports regressions of ETF-NAV returns on the lagged level of premium to control for mean-reversion, MKT,
SMB, HML and funding liquidity (NOISE) factors, estimated fund-by-fund using all available observations. T-statistics
for the mean are adjusted for cross-correlation as in Hameed, Kang and Viswanathan (2010). */**/*** denotes statistical
significance at the 10, 5 and 1 % level. βR2 is the average improvement in R-squared compared to the model where ETF-
NAV returns are only regressed against the lagged level of premium.
Daily horizon Weekly horizon Monthly horizon
Factor By style (a) (b) (a) (b) (a) (b)
MKT All -0.0193*** -0.0197*** -0.0050** -0.0052** -0.0036 -0.0016
Small -0.0204*** -0.0204*** -0.0048 -0.0047 -0.0079** -0.0046
Large -0.0184*** -0.0190*** -0.0041* -0.0044* -0.0016 -0.0004
Value -0.0216*** -0.0221*** -0.0053* -0.0055* -0.0049 -0.0037
Growth -0.0192*** -0.0194*** -0.0046** -0.0049** 0.0002 0.0002
SMB All 0.0056 0.0072 0.0066 0.0063 -0.0035 -0.0007
Small -0.0126* -0.0113* -0.0023 -0.0023 0.0021 -0.0049
Large 0.0123** 0.014*** 0.0078 0.0072* 0.0001 0.0016
Value 0.0075 0.010 0.0059 0.0054 0.0020 -0.0004
Growth 0.0088* 0.0102** 0.0054 0.0050 0.0002 0.0013
HML All -0.0116*** -0.0106*** 0.0030 0.0034 -0.0005 -0.0017
Small -0.0118** -0.0116** 0.0048 0.0047 -0.0017 -0.0034
Large -0.0091** -0.0076* 0.0029 0.0036 0.0010 0.0003
Value -0.0222*** -0.0211*** 0.0017 0.0021 0.0022 0.0013
Growth -0.0024 -0.0020 0.0041 0.0046 -0.0021 -0.003
NOISE All 0.0146* -0.0089 0.0134
Small 0.0100 0.0042 0.0221
Large 0.0171** -0.0165 0.0076
Value 0.0219** -0.0129 0.0079
Growth 0.0117* -0.0105 0.0131
βR2 All 0.080 0.082 0.019 0.032 0.064 0.102
N obs All 258,529 254,405 53,764 53,288 13,664 13,502
42
Table 6: Source of mispricing: ETF or NAV?
This table reports results from estimating the following pooled OLS regression on daily data:
3 3
, 1 , 10 0
E N
i t i k t k k t k i tk kR a b P c R e
where π π,π‘+1 is the raw ETF return (in Panel A), or the NAV return (in Panel B). PREM, or πππΈβπ, is the ETF premium
relative to NAV. Standard errors are adjusted for serial and cross-sectional correlation as in Driscoll and Kraay (1998). I
also provide an F-test for the hypothesis that the sum βbk equals zero. */**/*** denotes statistical significance at the 10, 5 and 1 percent level.
Sample:
Variables Full Sector Core Large Mid Small
PANEL A: Y = ETF return, t
PREM, t-1 -0.570* -0.511* -0.677 0.016 -0.850 -1.284**
(1.86) (1.76) (1.55) (0.03) (1.34) (2.48)
PREM, t-2 -0.964*** -0.860** -1.142*** -1.366** -1.113** -1.011**
(3.01) (2.60) (3.26) (2.53) (2.37) (2.48)
PREM, t-3 -0.352 -0.257 -0.531 -0.553 -0.897 -0.317
(0.92) (0.80) (0.94) (0.85) (1.22) (0.59)
PREM, t-4 0.071 0.015 0.200 0.348 0.402 -0.076
(0.20) (0.05) (0.44) (0.53) (0.69) (0.20)
ETF Ret, t-1 -0.091*** -0.095*** -0.086*** -0.091*** -0.058* -0.101***
(3.23) (3.50) (2.68) (2.75) (1.81) (2.89)
ETF Ret, t-2 -0.046 -0.043 -0.052 -0.056 -0.053 -0.047
(1.25) (1.25) (1.21) (1.24) (1.19) (1.13)
ETF Ret, t-3 -0.007 -0.009 -0.005 0.004 -0.011 -0.014
(0.24) (0.30) (0.15) (0.10) (0.30) (0.40)
ETF Ret, t-4 -0.014 -0.016 -0.011 -0.004 -0.016 -0.016
(0.42) (0.48) (0.30) (0.09) (0.42) (0.45)
F-test:
β ππ = 03π=0
7.79*** 6.91** 7.98*** 3.17* 3.84* 13.20***
R2 0.012 0.012 0.014 0.017 0.011 0.018
N obs 260,449 134,621 125,828 66,126 28,559 31,143
PANEL B: Y = NAV return, t
PREM, t-1 0.358 0.468 0.147 0.756 0.216 -0.489
(1.15) (1.62) (0.34) (1.54) (0.33) (0.93)
PREM, t-2 -1.040*** -0.921*** -1.238*** -1.414** -1.273** -1.102**
(3.25) (2.80) (3.42) (2.51) (2.59) (2.60)
PREM, t-3 -0.351 -0.251 -0.542 -0.551 -0.965 -0.329
(0.87) (0.72) (0.92) (0.80) (1.26) (0.60)
PREM, t-4 0.043 -0.005 0.157 0.365 0.380 -0.183
(0.12) (0.02) (0.32) (0.51) (0.62) (0.45)
NAV Ret, t-1 -0.090*** -0.094*** -0.085** -0.093*** -0.051 -0.099**
(3.13) (3.39) (2.61) (2.78) (1.57) (2.80)
NAV Ret, t-2 -0.051 -0.047 -0.057 -0.062 -0.058 -0.052
(1.35) (1.35) (1.30) (1.33) (1.30) (1.21)
NAV Ret, t-3 -0.008 -0.009 -0.007 0.002 -0.011 -0.017
(0.28) (0.33) (0.19) (0.04) (0.30) (0.50)
NAV Ret, t-4 -0.015 -0.017 -0.013 -0.004 -0.018 -0.019
(0.44) (0.49) (0.34) (0.10) (0.45) (0.53)
F-test:
β ππ = 03π=0
2.16 1.26 3.29* 0.78 1.50 7.61**
R2 0.014 0.014 0.014 0.020 0.011 0.015
N obs 259,800 134,350 125,450 65,904 28,445 31,101
43
Table 7: Comovement in relative trading activity and price impact
Daily shocks to relative turnover (price impact) for ETF i are regressed on equally-weighted shocks in relative turnover
(price impact) of other ETFs in the own- and distant styles:
1
, , , ,, , ,
1
1
, , , ,, , ,
1
,
,
i i j O i j DIi t OWN t j DIST t j
j
i i j O i j DIi t OWN t j DIST t j
j
TOi t
LIQi t
REL TO REL TO REL TO u
REL PI REL PI REL PI u
The regressions include concurrent, lagged and lead values for the factors. I report the average and median values for the
concurrent, lagged, lead, sum coefficients and the average R2; the percentage of funds with positive coefficients, the
percentage of funds with positive and significant coefficients, negative and significant coefficients. Test of statistical
significance for the mean is based on the cross-sectional t-statistic for the average coefficient, while the significance for the
median is based on a sign-test. */**/*** denotes statistical significance at the 10, 5 and 1 % level.
Own-style betas Distant-style betas
Statistic Conc. Lag Lead Sum Conc. Lag Lead Sum Avg. R2
PANEL A: Relative turnover
Mean 0.616*** 0.104*** 0.089*** 0.810*** 0.205*** -0.043*** -0.056*** 0.107*** 0.086
(26.51) (5.49) (5.13) (16.68) (10.79) (2.91) (3.50) (2.85) Median 0.606*** 0.089*** 0.075*** 0.689*** 0.162*** -0.041** -0.032** 0.073*** 0.084
% pos 100.00 71.95 65.85 94.51 82.32 40.24 37.20 57.93
% pos & sig 93.90 23.78 23.17 87.20 51.83 6.71 7.32 44.51
% neg & sig 0.00 11.59 4.88 0.61 0.61 18.29 15.24 20.73
PANEL B: Relative price impact
Mean 0.972*** -0.006 -0.012 0.955*** -0.082*** 0.012 0.020* -0.049 0.281
(42.66) (0.34) (1.03) (25.21) (4.38) (1.06) (1.78) (1.41) Median 0.982*** 0.030 -0.008 1.017*** -0.106*** 0.012 0.021 -0.063*** 0.257
% pos 100.00 54.88 48.17 96.34 32.93 53.66 56.10 46.34
% pos & sig 99.39 25.61 10.98 93.29 16.46 24.39 22.56 35.98
% neg & sig 0.00 28.66 22.56 1.83 43.90 15.24 15.24 42.68
44
Table 8: Explaining the degree of excess return comovement
This table reports results from regressions of the amount of return comovement (π πππ‘,π2 ) for ETF i on the following measures
of correlated demand shocks: commonality in abnormal trading activity (π πππ,πβ12 ), commonality in relative price impact
(π πππΌ,πβ12 ). Comovements are based on the model R2, or the fraction of model R2 attributable to the own and distant style
factors. R2 is estimated every month (m) using daily data. Other variables included are expense ratios, share
creation/redemption activity (CREATE), magnitude of average mispricing [abs(PREM)], monthly ETF and underlying
portfolio proportional quoted spreads (ETF QSPR, UND QSPR; signed to indicate liquidity), volatility of NAV returns
(STD(NAV)), Hu, Pan and Wang (2013) funding liquidity (NOISE). All variables are measured at the end of the previous
month except for the macro variables STD(NAV) and NOISE that are contemporaneous. */**/*** denotes statistical
significance at the 10, 5 and 1 % level. Standard errors are double-clustered by fund and calendar time.
Core style Sector style
Variables (1) (2) (3) (4) (5) (6) (7)
Exp. Ratio, m-1 -0.173*** -0.142** -0.143** -0.335*** -0.008 -0.315*** -0.154
(2.63) (2.20) (2.23) (5.02) (0.09) (5.53) (1.09)
CREATE, m-1 -6.901*** -6.595*** -6.425*** -4.453** -6.518*** -9.192*** -1.365
(5.10) (4.87) (4.79) (2.17) (4.29) (6.64) (1.33)
abs(PREM), m-1 -61.968*** -59.117** -61.518*** -73.541*** -42.255 1.333 -49.100**
(2.82) (2.53) (2.64) (2.72) (1.51) (0.08) (2.28)
ETF QSPR, m-1 6.748*** 5.896*** 5.815*** 6.113*** 4.601** 7.764*** 5.530***
(4.99) (4.48) (4.46) (4.46) (2.05) (5.84) (3.08)
UND QSPR, m-1 -3.351 -3.073 -2.955 -4.305* -2.070 -9.215*** -4.144*
(1.63) (1.53) (1.47) (1.75) (0.84) (3.48) (1.76)
STD(NAV), m 3.003** 3.057** 2.988** 3.591* 3.273** 0.046 3.247**
(2.22) (2.18) (2.10) (1.92) (2.19) (0.03) (2.04)
NOISE, m 1.740*** 1.657*** 1.662*** 1.712*** 1.322*** 1.424***
(3.97) (3.88) (3.86) (2.84) (3.31) (3.21)
π πππ,πβ12 0.077*** 0.049** 0.050 0.049 0.031 0.048**
(3.18) (2.04) (1.60) (1.50) (1.41) (2.10)
π πππΌ,πβ12 0.095*** 0.092*** 0.056*** 0.103*** 0.097*** 0.048***
(6.77) (6.46) (3.06) (5.06) (6.25) (4.13)
Dummies
Sector, style YES YES YES YES YES YES YES
Calendar time NO NO NO NO NO YES NO
ETF NO NO NO NO NO NO YES
R2 0.222 0.235 0.233 0.225 0.108 0.291 0.342
N obs 11,843 11,794 11,689 5,722 5,967 11,689 11,689